# How do you solve 9x^2 -18x - 1 =0 by completing the square?

Apr 6, 2016

The solutions are:
color(green)(x = (sqrt 10 + 3)/3 ,  color(green)(x = (-sqrt 10 + 3) / 3

#### Explanation:

$9 {x}^{2} - 18 x - 1 = 0$

$9 {x}^{2} - 18 x = 1$

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

$9 {x}^{2} - 18 x + 9 = 1 + 9$

${\left(3 x\right)}^{2} - 2 \cdot 3 x \cdot 3 + {3}^{2} = 10$

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

${\left(3 x - 3\right)}^{2} = 10$

$3 x - 3 = \sqrt{10}$ or $3 x - 3 = - \sqrt{10}$

color(green)(x = (sqrt 10 + 3)/3 or  color(green)(x = (-sqrt 10 + 3) / 3