In week √36 of precal we learned about quadratic equations. Quadratic equations are unique in the way that they will always be AX^2 +BX + C = 0. An interesting thing about quadratics is that there are different ways of solving them. You can factor them or you can “complete the square”. to complete the square you move the number in the C spot over, find the number that would make it a perfect square, then add it to both sides and simplify further from there. I will go over how to do that, including how to find what number will make it a perfect square.

Lets use the equation X^2+6x+8=0 as an example. To start, we subtract the 8 from the left side and the right side

X^2+6x=-8

Next we find what number goes into the C spot. In this certain equation when there is no coefficient to X^2, it will be half of the coefficient of B squared. In this it will be 3^2 which is 9. We then add 9 to both sides and it will look like this

X^2+6x+9=1

Now we can easily factor the left side to simplify the equation.
(x+3)^2=1

Now we must remove the exponent on the left side and we can do so by rooting both sides

√(x+3)^2=√1 = X+3 = +/-1

because of how rooting works the 1 is either positive or negative, meaning there are 2 answers to these types of equations.

X1=-2    X2=-4

And this is how you solve quadratic equations by “completing the square”.