How do you solve x^2+10x-1=0 using completing the square?

Jun 15, 2015

$x = - 5 \pm \sqrt{26}$

Explanation:

${x}^{2} + 10 x - 1 = 0$

simplify by moving the constant to the right side
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} + 10 x = 1$

complete the square
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} + 10 x + {\left(\frac{10}{2}\right)}^{2} = 1 + {\left(\frac{10}{2}\right)}^{2}$

rewrite as a square and simplify the right side
$\textcolor{w h i t e}{\text{XXXX}}$${\left(x + 5\right)}^{2} = 26$

take the square root of both sides
$\textcolor{w h i t e}{\text{XXXX}}$$x + 5 = \pm \sqrt{26}$

subtract $5$ from both sides to isolate $x$
$\textcolor{w h i t e}{\text{XXXX}}$$x = - 5 \pm \sqrt{26}$