# How do you solve using the completing the square method x^2-10x-4=0?

Feb 26, 2016

$x = 5 \pm \sqrt{2}$

#### Explanation:

${x}^{2} - 10 x - 4 = 0$

Notice 10x

This can be our $2 a b$ term

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$

-2ab = -10x

ab =5x
We have a = x

b = 5

${x}^{2} - 10 x + {5}^{2} - {5}^{2} - 4 = 0$

${\left(x - 5\right)}^{2} = 4 + 25 = 29$

$x - 5 = \pm \sqrt{2}$

$x = 5 \pm \sqrt{2}$