# How do you solve the equation x^2+8x+16=7 by completing the square?

May 20, 2018

color(indigo)(x = sqrt7 - 4, color(maroon)(x = -sqrt7 - 4

#### Explanation:

${x}^{2} + 8 x + 16 = 7$

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

$\therefore L H S = {x}^{2} + 2 \cdot 4 \cdot x + {4}^{2} = {\left(x + 4\right)}^{2}$

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

$x + 4 = \pm \sqrt{7}$, taking root on both sides

color(maroon)(x = +-sqrt7 - 4