Question

How do you complete the square for `x^2 + 12x`?

Answer 1

The answer is `x=0`; `x=-12` .

Problem: Complete the square for `x^2+12x`.

Rewrite the equation as a trinomial.

`x^2+12x+0`

Move 0 to the right-hand side.

`x^2+12x=0`

Divide the coefficient of the `x`-term by 2, then square the result. Add the result to both sides.

`12/2=6`; `6^2=36`

`x^2+12x+36=36`

Factor the perfect square trinomial `x^2+12x+36` on the left-hand side.

`(x+6)^2=36`

Take the square root of both sides and solve for `x`.

`sqrt((x+6)^2)=+-sqrt36` =

`x+6=+-6`

`x=-6+6=0`

`x=-6-6=-12`

Check

If `x=0`:

`(0)^2+12(0)=0`

`0=0`

If `x=-12`:

`(-12)^2+12(-12)=0`

`144-144=0`

`0=0`