# How do you solve using the completing the square method x^2 + 4x = 7?

Feb 26, 2016

See solution below.

#### Explanation:

$1 \left({x}^{2} + 4 x + m\right) = 7$

$m = {\left(\frac{b}{2}\right)}^{2}$

$m = {\left(2\right)}^{2}$

$m = 4$

$1 \left({x}^{2} + 4 x + 4\right) = 7$

Factor as a perfect square trinomial.

$1 {\left(x + 2\right)}^{2} = 7$

$\left(x + 2\right) = \pm \sqrt{7}$

$x = \pm \sqrt{7} - 2$

Don't forget the $\pm$ sign with the square root.

Practice exercises:

Solve for x by completing the square.

a) $3 {x}^{2} + 12 x - 8 = 0$

b) $2 {x}^{2} + 7 x + 15 = 0$

Good luck!