Quadratic Formula
Let say you're given this equation of 5 x
Raised to the second power plus nine x minus six equals to zero.
And they want us to solve for x.
Before you use the quadratic formula,
you need to see if this
quadratic equation is factorable or not.
Before you use the quadratic formula.
So, to factor this equation out.
The first thing you need to do is.
Let say you're given this quadratic equation and they want us to solve for x, righ?
So, the first thing you need to do is to try to factor this quadratic equation out.
So, you put two parentheses.
For the first term right here, five times one will be five x square.
As for the negative six, six times one equals to, positive six times negative one equals to negative six.
And you have to make sure.
That will equals to this number right here, the middle term right here.
So, positive six times x equals to six x.
Negative one times five x equals to minus five x.
So, six x minus five x equals to x.
Which is not the same as nine x.
So, this.
Whole expression times this whole expression right here.
Is not a factor for this  quadratic equation.
The next factor
you could try out is .
five x minus six times x plus one.
Five x times x equals five x square which matches the first term of the quadratic equation.
And negative six times positive one equals to negative six.
So, it matches the last consonant of the quadratic equation.
And you have to check if it equals to nine x.
So, you take negative six x times.
Plus the five x times the one.
So, negative six x plus five x equals to negative x.
So, this factor right here is not a factorable of this quadratic equation.
The next thing is to try another factor.
To see if it's factorable or not.
I could try like five x times x matches this five x square.
And negative three times positive two matches the negative six.
And we have to check if this whole
factored form right here matches the middle term of the quadratic equation or not.
So, to check that.
You take negative three x
Negative three times x which is negative three x.
Two, positive two times
five x is positive ten x.
So, negative three x plus ten x equals to seven x.
So, the seven x doesn't matches this given quadratic equation of nine x.
So, this is not a factor of that.
The last factor you could try is this one.
And when you do this one, the five x times x matches the original equation of five x square.
Positive three x , positive three times x, is positive three x.
MInus the five x times negative two which is negative ten x.
And when you do an addition of it, three x minus ten x equals negative seven x.
Negative seven x doesn't match this quadratic equation of the middle term of positive nine x.
So, notice all these factor that we.
did just now.
Is not a factor of these quadratic equation.
So, the last method  to use is to use the quadratic formula.
The quadratic formula is x equals to negative b
plus or minus radical b square minus four times  a times c. Divide by two a.
So, the a will be the five.
The b will be the nine.
The c will be the negative six.
Once you have this letter
All you need to do is plug it back into the quadratic formula.
So, the b will be negative nine.
Plus or minus radical b square which is nine square minus.  You always put the minus right here.
Because if you don't, when you do the calculation it'll be very confusing.
So, always put the minus.
Then put down the four.
The a is five.
The c will be negative six according to the given quadratic equation.
And the a will be five right here.
So, once you plug in all the numbers.
It's time to calculate this whole expression.
So, negative nine will stay the same.
plus or minus always stay the same.
The radical stay the same.
Nine square is eighty-one.
Put a minus, always put a minus.
And then four times five times negative six.
is negative one-hundred twenty.
Divide by two times five which is ten.
So, this one is the same, this one is the same.
Radical eighty-one, the negative times a negative will become positive.
So, it is positive one-hundred twenty.
Divide by ten.
Eighty-one plus one-hundred twenty will be two-hundred one.
So, it will be negative nine plus or minus radical two-hundred one divide by ten.
Once you have this calculation,  this plus or minus could be seperate out into two answer.
So, the first one will be negative nine plus radical two-hundred one divide by ten.
The second one will be negative nine minus radical two-hundred one divide by ten.
So, the answer for this quadratic equation.
It will be these two x.  The first one will be this one and the second one will be this one.
And notice the sign is different.
