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

May 17, 2015

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

Problem: Complete the square for ${x}^{2} + 12 x$.

Rewrite the equation as a trinomial.

${x}^{2} + 12 x + 0$

Move 0 to the right-hand side.

${x}^{2} + 12 x = 0$

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

$\frac{12}{2} = 6$; ${6}^{2} = 36$

${x}^{2} + 12 x + 36 = 36$

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

${\left(x + 6\right)}^{2} = 36$

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

$\sqrt{{\left(x + 6\right)}^{2}} = \pm \sqrt{36}$ =

$x + 6 = \pm 6$

$x = - 6 + 6 = 0$

$x = - 6 - 6 = - 12$

Check

If $x = 0$:

${\left(0\right)}^{2} + 12 \left(0\right) = 0$

$0 = 0$

If $x = - 12$:

${\left(- 12\right)}^{2} + 12 \left(- 12\right) = 0$

$144 - 144 = 0$

$0 = 0$