# How do you solve using completing the square method x^2-6x-7=0?

May 3, 2016

The solutions are:
color(green)(x = 7 ,  color(green)(x = -1

#### Explanation:

${x}^{2} - 6 x - 7 = 0$

${x}^{2} - 6 x = 7$

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

x^2 - 6x + color(blue)(9) = 7 + color(blue)(9

${x}^{2} - 2 \cdot x \cdot 3 + {3}^{2} = 16$

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

${\left(x - 3\right)}^{2} = 16$

$x - 3 = \sqrt{16}$ or $x - 3 = - \sqrt{16}$

$x - 3 = 4$ or $x - 3 = - 4$

$x = 4 + 3$ or $x = - 4 + 3$

color(green)(x = 7 ,  color(green)(x = -1