# How do you solve x^2+16x=17 by completing the square?

Apr 13, 2016

color(green)(x = 1  ,  color(green)(x = -17

#### Explanation:

${x}^{2} + 16 x = 17$

To write the Left Hand Side as a Perfect Square, we add 64 to both sides:

${x}^{2} + 16 x + 64 = 17 + 64$

${x}^{2} + 2 \cdot x \cdot 8 + {8}^{2} = 81$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get
${\left(x + 8\right)}^{2} = 81$

$x + 8 = \sqrt{81}$ or $x + 8 = - \sqrt{81}$

$x + 8 = 9$ or $x + 8 = - 9$

$x = 9 - 8 = 1$ or $x = - 9 - 8$

color(green)(x = 1  or  color(green)(x = -17