# How do you solve #y=5x^2+20x+23# using the completing square method?

##### 1 Answer

#### Explanation:

I will assume that we want to solve the equation in the sense of expressing possible values of

If you actually just wanted to know the zeros, we can then put

Given:

#y = 5x^2+20x+23#

We will perform a sequence of steps to isolate

First divide both sides by

#y/5 = x^2+4x+23/5#

If we take half of the coefficient of

#(x+2)^2 = x^2+4x+4#

which matches the right hand side of our equation in the first two terms.

So we can proceed as follows:

#y/5 = x^2+4x+23/5#

#color(white)(y/5) = x^2+4x+4-4+23/5#

#color(white)(y/5) = (x+2)^2+3/5#

Subtracting

#(y-3)/5 = (x+2)^2#

Transposed:

#(x+2)^2 = (y-3)/5#

Take the square root of both sides, allowing for the possibility of either sign of square root to get:

#x+2 = +-sqrt((y-3)/5)#

Finally subtract

#x = -2+-sqrt((y-3)/5)#

If we put

#x = -2+-sqrt((0-3)/5) = -2+-sqrt(-3/5) = -2+-sqrt(3/5)i = -2+-sqrt(15)/5i#