# How do you solve using the completing the square method x^2 - 8x - 3 = 0?

Mar 23, 2016

The solutions are:
color(green)(x = sqrt 19 + 4
 color(green)(x = -sqrt 19 + 4

#### Explanation:

${x}^{2} - 8 x - 3 = 0$

${x}^{2} - 8 x = 3$

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

${x}^{2} - 8 x + 16 = 3 + 16$

${x}^{2} - 2 \cdot x \cdot 4 + {4}^{2} = 19$

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

${\left(x - 4\right)}^{2} = 19$

$x - 4 = \sqrt{19}$ or $x - 4 = - \sqrt{19}$

color(green)(x = sqrt 19 + 4 or  color(green)(x = -sqrt 19 + 4