# How do you solve using the completing the square method x^2+6x=7?

Apr 18, 2016

Create a perfect square trinomial on the left side, and your solution is not far away!

#### Explanation:

First, the lead coefficient should = 1 to make this easiest.
Then, take half of the linear coefficient, then square it. Add to both sides:
${x}^{2} + 6 x + 9 = 7 + 9$
Factor the left:
${\left(x + 3\right)}^{2} = 16$
Take the square root of both sides:
$\sqrt{{\left(x + 3\right)}^{2}} = \sqrt{16}$
Left side inverse operations undo each other, on the right side, don't forget the $\pm$ on the right!

$x + 3 = \pm 4$

so $x + 3 = 4$ or $x + 3 = - 4$

so x = 1 or -7.