# How do you solve using the completing the square method x^2 - 6x - 16=0?

Mar 22, 2016

The solutions are:
$x = 8$ and
$x = - 2$

#### Explanation:

${x}^{2} - 6 x - 16 = 0$

${x}^{2} - 6 x = 16$

To write the Left Hand Side as a Perfect Square, we add 9 to both sides:

${x}^{2} - 6 x + \textcolor{b l u e}{9} = 16 + \textcolor{b l u e}{9}$

${x}^{2} - 2 \cdot x \cdot 3 + {3}^{2} = 25$

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

${\left(x - 3\right)}^{2} = 25$

$x - 3 = \sqrt{25}$ or $x - 3 = - \sqrt{25}$

$x = 5 + 3 = 8$ or $x = - 5 + 3 = - 2$

The solutions are:
$x = 8$ and
$x = - 2$