# How do you solve x^2+10x-9=0?

Dec 13, 2016

$x = - 5 \pm \sqrt{34}$

#### Explanation:

${x}^{2} + 10 x - 9 = 0$

is in the form:

$a {x}^{2} + b x + c = 0$

where $a = 1$, $b = 10$ and $c = - 9$

Use the quadratic formula to find:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\textcolor{w h i t e}{x} = \frac{- 10 \pm \sqrt{{10}^{2} - 4 \left(1\right) \left(- 9\right)}}{2 \cdot 1}$

$\textcolor{w h i t e}{x} = \frac{- 10 \pm \sqrt{100 + 36}}{2}$

$\textcolor{w h i t e}{x} = \frac{- 10 \pm \sqrt{136}}{2}$

$\textcolor{w h i t e}{x} = \frac{- 10 \pm \sqrt{{2}^{2} \cdot 34}}{2}$

$\textcolor{w h i t e}{x} = \frac{- 10 \pm 2 \sqrt{34}}{2}$

$\textcolor{w h i t e}{x} = - 5 \pm \sqrt{34}$