Quadratic Formula - Using the Formula
If a x squared plus b x plus c equals zero,
then x equals negative b plus or minus the square root of b squared minus 4 a c all over 2 a.
I recommend that you write down this formula and that you put it in front of you,
so that you can be able to use it until you get it memorized.
You will have to have this memorized.
Let's take a look at example one and see how this works.
Our six is going to be our a, our b is seven and our c is a negative three.
Our b for the first part is always going to be the opposite sign,
so because we have a positive seven, we're going to use a negative seven.
Put in our plus or minus the square root of b squared.
I do not need to worry about my sign here, because anything squared is going to be positive.
So we have minus four times our a, which is six times our c,
which is a negative three all over two times our a which was six.
Now we need to start figuring this out.
So we have negative seven plus or minus, seven squared is forty nine.
I have two negatives here which is going to give me a plus, so it'll be plus.
And since I'm doing this by hand, I'm going to do a four times three,
which would give me twelve, and twelve times six is seventy two.
All over two times six which is twelve, well, forty nine and seventy two.
Well that's going to give me eleven, seven.
So twelve, 121, so I get a negative seven plus or minus the square root of 121 all over twelve.
Now this is if you got your, all your squares memorized.
You would recognize that 121 is a perfect square,
and that the square root of that then would be negative seven plus or minus eleven, all over twelve.
I'm going to rewrite this so I have negative seven plus eleven over twelve,
and negative seven minus eleven over twelve.
Okay, negative seven plus eleven is going to give me four-twelfths,
the negative seven minus eleven will give me negative eighteen-twelfths.
I'm going to reduce those.
So x is going to be one-third and a negative, let's see both of those are divisible by six,
so three-halves and I've solved example one.
Let's take a look at our example two.
Negative five is going to be my a, an invisible one for my b here and two is going to be my c.
Now because my b is negative, I'm going to have a positive here,
so it'll be one plus or minus the square root of one squared minus four times our a
which is negative five times our c, which is two all over two times are a.
So simplifying this, I get one plus or minus the square root of one.
Let's see two negatives that'll be positive, so b plus twenty times two which would be forty
all over negative ten, and that's going to give me one plus or minus
the square root of forty one all over negative ten.
Forty one is a prime number it will not simplify so this would be my answer.
If you are asked to give your answer in solution set,
that means you would answer it as one plus the square root of forty one over negative ten,
or one and I should say one minus the square root of forty one over negative ten.
