How do you solve x^2+8x=9 by completing the square?

Apr 26, 2016

The solutions are:
color(green)(x = 1 , x=-9

Explanation:

${x}^{2} + 8 x = 9$

To write the Left Hand Side as a Perfect Square, we add 16 to both sides:

${x}^{2} + 8 x + 16 = 9 + 16$

${x}^{2} + 2 \cdot x \cdot 4 + {4}^{2} = 25$

Using the Identity color(blue)((a+b)^2 = a^2 + 2ab + b^2, we get,

${\left(x + 4\right)}^{2} = 25$

$x + 4 = \sqrt{25}$ or $x + 4 = - \sqrt{25}$

$x + 4 = 5$ , $x + 4 = - 5$

$x = 5 - 4 = 1$ ,

$x = - 5 - 4 = - 9$

The solutions are:
color(green)(x = 1 , x=-9