
English: 
Ok, in this video I want to talk about completing the square.
I'm going to complete the square in solving a quadratic equation.
This will the first two examples. This one will be  a little easier.
Here we're going to solve the quadratic equation, x^2 - 6x + 8
You can definitely factor this one without too much trouble
But, I wanna talk about understanding the procedure here.
So, I want to do it the longer way.
The first thing you want to do is you look at the x-terms.
And you want the coefficient of the x-squared term to equal 1, which it does in this case.
If not, you have to factor it out and I'll do something like that in a separate example.
We have this condition, so what we then do is we just kind of stick that in a set of parentheses, the first two.

Czech: 
V tomto videu budu mluvit o doplnění na čtverec.
Budu doplňovat na čtverec a řešit kvadratickou rovnici.
Toto bude první ze dvou příkladů. Tento bude o trochu jednodušší.
Budeme řešit kvadratickou rovnici x na druhou mínus šest x plus osm.
Určitě jí dokážete rozložit bez velkého úsilí, ale já bych chtěl mluvit o pochopení postupu.
Pojďme to tedy dělat delší cestou.
První věc, kterou chcete udělat, je podívat se na členy s x, které se zde objevují.
Chcete koeficient...
Chcete koeficient u členu x na druhou roven jedné, což je v tomto případě.
Kdyby ne, musíte ho vytknout. Něco takového udělám v jiném příkladě.
Čili máme tuto podmínku.
Co uděláme potom je, že první dva členy umístíme do závorek.

Portuguese: 
Ok, nesse vídeo eu quero falar sobre "completar quadrados"
E... vou completar quadrados e resolver uma equação do segundo grau
Esse será o primeiro de dois exemplos e será um pouco mais fácil, então
Aqui nós vamos resolver a equação do segundo grau:    x² - 6x + 8
E... com certeza você pode fatorá-la sem muitos problemas
Mas eu gostaria de falar sobre "como entender o método" aqui, então
Vamos fazer então pelo "caminho mais longo"
A primeira coisa que você deve fazer é
Você olha para os termos "x" que estão lá
E você quer que o coeficiente
Você quer que o coeficiente do termo x² seja igual a 1
Que nesse caso é (verdade), se não for, você tem que fatorar
E eu farei algo do tipo no segundo exemplo
Então temos essa condição
O que faremos então é colocar isso dentro de parentêsis

English: 
The first thing you want to do is, you look at the "x" terms
basically that are in there and you want the coefficient
you want the coefficient of the "X" squared term to equal one
which it does in this case
if not , you have to factor it out.and i'll do something like that
in a separate example
so we have this condition. What we then do is

Portuguese: 
Os dois primeiros; deixe um pouco de espaço
Então vou escrever meu +8, dar mais um pouco de espaço
igual a 0
Então, toda a ideia de completar quadrados é
você olha pra qualquer número que esteja em frente ao termo "x"
então, nesse caso o número em frente a "x", o coeficiente no termo "x" é -6
Então dividimos esse número pela metade (1/2), você sempre dividirá por 2
Então metade de -6 será -3
Então o que você faz é elevar ao quadrado
E você coloca esse número novamente lá em cima
Elevando ao quadrado, obtemos +9
Ok, então, na verdade, colocamos um número totalmente novo, que não estava lá antes
Colocamos esse 9 positivo que não estava lá
O jeito que temos para nos livrarmos dele, nesse caso é
Basicamente, imagine se livrando dos parentêses

English: 
stick in a set of parenthases with the first two, give yourself a little space
and then i'm going to write my plus eight, give myself a little space, equals zero
so the whole point of how you complete the square is, you look at
whatever number is front of the "X" term,  so in this case, the number in front of the "X"
the coefficient, on the "X " term is one-half (1/2, .5). we then take one half of that number.we always take one half of it
so one half of negative six, is negative 3.
and then what you do is,
you square it, and put that number back inside of there. so if we square it
we get positive nine.
okay, so we've actually thrown in a brand new number that wasn't there
before, we put in this positive nine.
that wasn't there
the way we can get rid of it, in this case,
is, I mean , basically,
you're just getting rid of the parenthasese
we would get back the original thing

Czech: 
Nechte si trochu místa a pak napíšu mých plus osm, nechám si trochu místa, rovná se nule.
Celá věc je v tom, způsob jak doplníte na čtverec je, že se podíváte na číslo, které je před členem s x.
V tomto případě číslo před x, koeficient členu s x, je jedna polovina [CHYBA, má být -6]
Z toho vezmeme jednu polovinu. Čili vždy vezmete jednu polovinu.
Jedna polovina mínus šest je mínus tři.
Co uděláte potom je, že umocníte na druhou a dáte to číslo zpět dovnitř.
Čili pokud umocníme, dostaneme plus devět.
Dobře. Vlastně jsme vytvořili zbrusu nové číslo, které tam dříve nebylo.
Přidali jsme těchto plus devět, které tam nebyly.
Způsob, jakým se jich můžeme zbavit v tomto případě je...
V podstatě si představte, že tu nejsou závorky.

English: 
Give yourself a little space
And then I'm going to write my +8, give myself a little space, equals 0.
The whole point of the way you complete the square is you look at what ever number is in front of the x-term.
In this case the number in front of the x, the coefficient on the x-term, is one half.
We then take one-half of that number. So you always take one-half of it.
So one-half of negative 6 will be negative 3
And then what you do is you square it
And then you put that number back inside of there.
So if we square it we get positive 9
So we've actually thrown in a brand new number that wasn't there before. We put in this positive 9.
The way that we can get rid of it in this case, is basically imagine getting rid of the parentheses

English: 
except our plus nine would be there
well to cancel it out,we are going to subtract nine. okay,
notice this is all happening on the left side of the equals sign
okay so now, we just simplify down a little bit more
and the point is, you can write the stuff in parenthases as a perfect square
it actually factors down as "x"  minus three , times "x" minus three
okay, and again, if you take whatever one half of the coefficient
on the "X" term was,
it was a negative three, that will go into the parenthesis.
positive eight minus nine, is negative one.
equals zero
now we write the first part, as "x" minus three squared
minus one equals zero
again, we are trying to solve a quadratic equation here.
what we do at this point is you now simply
add the one to both sides

English: 
We would get back the original thing, except our plus 9 would be there.
Well, to cancel it out we're going to subtract 9.
Notice this is all happening on the left side of the equal sign
So now, we just simplify down a little bit more.
The point is you can write this stuff in parentheses as a perfect square.
This actually factors now as x minus 3, times x minus 3.
And again, if you take what ever one half of the coefficient on the x-term was, it was a negative 3, that's what will go inside the parentheses.
Positive 8, minus 9, is negative 1, equals 0
Now we write the first part as x minus 3, squared.
Minus 1, equals 0
Again, we are trying to solve a quadratic equation.
What we do at this point is simply add 1 to both sides.

Czech: 
Dostaneme původní věc kromě těch plus devět.
Abychom je vyrušili, odečteme devět.
Všimněte si, že se to celé odehrává na levé straně rovnice.
Nyní zjednodušíme o trochu více.
A věc je v tom, že můžete napsat to v závorce jako čtverec.
Toto se vlastně rozloží na x mínus tři krát x mínus tři.
A znovu: když vezmete polovinu z koeficientu u členu s x, což bylo mínus tři, tak ta půjde do těch závorek.
Plus osm mínus devět je mínus jedna, rovná se nule.
Teď napíšeme první část jako x mínus tři na druhou
mínus jedna rovná se nule.
Tady se pokusíme vyřešit kvadratickou rovnici.
Co uděláme v tomto místě je, že jednoduše přidáme jedna na obou stranách.

Portuguese: 
Nós teríamos de volta a expressão original, exceto o +9, que estaria lá
Bem, para cancelar, vou subtrair 9, ok?
Note que tudo isso está acontecendo do lado esquerdo da igualdade
Ok, então agora vamos somente simplificar um pouco mais
A ideia então é que você pode escrever o que está nos parentêses como um "quadrado perfeito"
Pode agora ser fatorado para: (x-3) multiplicando (x-3)
E novamente, se você pega a metade do coeficiente de x, que era o -3
É isso que vai dentro dos parêntesis
(+8 -9) é -1, igual a 0
Agora, escrevemos a primeira parte como (x-3)²
-1 =0
Ok, então estamos tentando resolver uma equação do segundo grau aqui
O que fazemos nesse ponto é que agora
você adiciona 1 em ambos os lados

Czech: 
Čili x mínus tři na druhou se rovná plus jedné.
A celé věc v řešení kvadratické rovnice pomocí doplnění na čtverec je v kroku, ke kterému se právě blížíme.
Protože co uděláme je, že vezmeme odmocniny z obou stran.
Vezmeme odmocniny z obou stran.
x mínus tři na druhou rovná se odmocnině z pravé strany.
Jelikož jsme odmocňovali, měli bychom přidat plus-mínus na jednu stranu.
Nalevo, pokud vezmete odmocninu z druhé mocniny, dostaneme jen x mínus tři.
A to se rovná buď plus nebo mínus jedné.
Čili teď máme dvě oddělené rovnice, které musíme vyřešit.
Jedna z rovnic, které musíme vyřešit, bude x mínus tři se rovná plus jedné.
A druhá rovnice, kterou musíme vyřešit, bude x mínus tři se rovná mínus jedné.

Portuguese: 
(x-3)² = +1
E toda a ideia de resolver uma equação do segundo grau pelo método de "completar quadrados"
É chegar no passo que estamos agora
Porque o que faremos agora é tirar a raiz quadrada em ambos os lados
Então se pegarmos a raiz quadrada dos dois lados:
Raiz de (x-3)² igual a raiz do lado direito
ok, então quando tiramos a raiz, devemos colocar o sinal de "mais ou menos" em um dos lados
Na esquerda, se tirarmos a raiz de algo ao quadrado, vamos obter (x-3)
E isso será igual a 1, positivo ou negativo
Agora teremos duas equações separadas para resolver
Uma das equações que temos para resolver é x - 3 = +1
E a outra equação que temos para resolver é x - 3 = -1

English: 
so "x" minus three squared ,
equals positive one
and the whole point of solving a quadratic equation by completing the square,
is getting to the step we are at right now
'cause what we are going to do is we are going to take the square root of
both sides, so if we take the square root of both sides, "x" minus three
squared,
equals the square root of the right side
okay, so once we take the square roots, we should put a positive
or negative on one side
on the left, if we take the square root,
of a quantity squared,
you're left with the inside, "x" minus 3
equals either positive, or negative one.
so now we get our two separate equations that we now have to solve
one of the equations we will
have to solve will be x minus 3
equals positive  one
and the other equation we'll have to solve
will be x minus three equals negative one.

English: 
So, x minus 3, squared, equals positive 1.
The whole point of solving a quadratic equation by completing the square, is getting to step where we are at right now.
We're going to take the square root of both sides.
So if we take the square root of both sides: x minus 3 , squared, equals the square root of the right side.
So once we take square roots, we should put a positive or negative on one side
On the left, if you take the square root of a quantity squared, we'll just get the x minus 3.
And this will equal either positive or negative 1.
Now we get our two separate equations that we have to solve.
One of the equations that we have to solve will be x minus 3, equals positive 1.
The other equation we have to solve will be x minus 3, equals negative 1.

English: 
So we simply add 3 in both cases.
And we'll get x equals positive 4 as one of our solutions.
If you add positive 3 to the other side, we'll get x equals positive 2 as our other solution.
And you can check that if you plug 2 and 4 into the original equation, you will get 0 out.
All right, this was example one. In my extra example I'm going to change the coefficients on the x-squared
Just to make it a bit more tedious.
Stick around if you need to see that example. It should be close by.

English: 
so well will simply add three in both cases
and we'll get "X" equals positive four. as one of our solutions
if you add positive three to the other side,
we'll get "X" equals positive two
as our other solution
and you can check that if you plug a
two and four into the original equation,
you will get zero.
alright, so this will be example one
in my extra example I will change the coefficient
on the x squared
to make it a little more tedious
stick around if you need to see that example,  it should be close by

Portuguese: 
ok, então vamos simplesmente adicionar 3 em ambos os casos
E vamos obter x = +4, como uma das nossas soluções
Adicionar +3 no outro lado e teremos x = +2 , como nossa outra solução
Você pode checar que substituindo...
... 2 e 4 na equação original, você terá 0 (como resultado)
Então esse será meu exemplo 1
E no meu exemplo extra, eu vou mudar o coeficiente de x²
Para torná-lo um pouco mais tedioso
Continue aqui, caso queira ver o exemplo, que deve estar próximo.

Czech: 
Jednoduše přidáme tři v obou případech
a dostaneme x se rovná plus čtyřem jako jedno z našich řešení.
Když přidáte plus tři na druhou stranu, dostaneme x se rovná plus dvě jako naše další řešení.
A můžete zkontrolovat, že pokud dosadíte dvě a čtyři do původní rovnice, dostanete nulu.
Dobře, čili toto bude příklad jedna a v mém dalším příkladu změním koeficient u x na druhou.
Tím to jenom udělám trochu zdlouhavější.
Zůstaňte poblíž, pokud potřebujete vidět ten příklad, měl by to být nedaleko.
