# How do you solve sqrt(x^2+8x-9)=x?

##### 3 Answers
Mar 10, 2018

$x = \frac{9}{8}$

#### Explanation:

$\sqrt{{x}^{2} + 8 x - 9} = x$

Squaring both sides,
${x}^{2} + 8 x - 9 = {x}^{2}$

Subtracting ${x}^{2}$ from both sides,
$8 x - 9 = 0$
$8 x = 9$
$x = \frac{9}{8}$

Mar 10, 2018

$x = \frac{9}{8}$

#### Explanation:

$\textcolor{b l u e}{\text{square both sides}}$

$\Rightarrow {\left(\sqrt{{x}^{2} + 8 x - 9}\right)}^{2} = {x}^{2}$

$\Rightarrow \cancel{{x}^{2}} + 8 x - 9 = \cancel{{x}^{2}}$

$\Rightarrow 8 x = 9 \Rightarrow x = \frac{9}{8}$

$\textcolor{b l u e}{\text{As a check}}$

$\Rightarrow \sqrt{{\left(\frac{9}{8}\right)}^{2} + 8 \left(\frac{9}{8}\right) - 9}$

$= \sqrt{\frac{81}{64} \cancel{+ 9} \cancel{- 9}} = \frac{9}{8} = \text{ right side}$

$\Rightarrow x = \frac{9}{8} \text{ is the solution}$

Mar 10, 2018

$x = \frac{9}{8}$

#### Explanation:

We can square both sides of the equation.

$\sqrt{{x}^{2} + 8 x - 9} = x$

${x}^{2} + 8 x - 9 = {x}^{2}$

$8 x - 9 = 0$

$8 x = 9$

$x = \frac{9}{8}$