# How do you solve this quadratic equation for completing the square?: 4x^2 + 12x -7=0

*print*Print*list*Cite

Expert Answers

steveschoen | Certified Educator

Hi, Rosey,

There can be a couple of ways to do this. Myself, I like to add 7 to both sides first. That gives us:

4x^2 + 12x = 7

Then, I divide each side by 4. That gives us:

x^2 + 3x = 7/4

Because, dividing the left side by 4, you have to divide 4x^2 and 12x by 4, both of them.

Then, you take half of 3 and square that result. Half of 3 is 1.5. Squaring that, we have 2.25. We add that to each side. Thus:

x^2 + 3x + 2.25 = 4

That 2.25 allows the left side to be factored into (x+1.5)^2

(x+1.5)^2 = 4

Taking the square root of each side:

x+1.5 = +-2

subtracting 1.5 from each side:

x = -1.5 +- 2 = -3.5, 0.5

So, x = -3.5 and x = 0.5

Good Luck, Rosey. I hope you understand the method.

Till Then,

Steve