# Find the solution to the equation x- square root of 8x+15=0?

Apr 21, 2018

$\setminus \textcolor{f u c h s i a}{\setminus} \textrm{E \mathrm{di} t e d}$answer
$x = 4 - \setminus \sqrt{31}$, $x = 4 + \setminus \sqrt{31}$

$\setminus \textcolor{t e a l}{\setminus} \textrm{O r i g \in a l}$answer
$x = - \frac{15}{8} \mathmr{and} x = - 1 \frac{7}{8}$

## $\setminus \textcolor{f u c h s i a}{\setminus} \textrm{E \mathrm{di} t e d}$solution

Assuming you meant $x - \sqrt{8 x + 15} = 0$

• Identify square root
$x - \setminus \textcolor{c r i m s o n}{\sqrt{8 x + 15}} = 0$
• Move the red part to the right side
$x = \setminus \textcolor{c r i m s o n}{\setminus \sqrt{8 x + 15}}$
• Now, let's square both both sides
${x}^{2} = {\left(\sqrt{8 x + 15}\right)}^{2}$
${x}^{2} = 8 x + 15$
• Move everything to the left
${x}^{2} - \left(8 x + 15\right) = 0$
${x}^{2} - 8 x - 15 = 0$
• Solve quadratic (see steps here)
$x = 4 \setminus \pm \setminus \sqrt{31}$
also written as $x = 4 - \setminus \sqrt{31}$, $x = 4 + \setminus \sqrt{31}$

## $\setminus \textcolor{t e a l}{\setminus} \textrm{O r i g \in a l}$solution

Assuming you meant $\sqrt{8 x + 15} = 0$

Now, let's square both both sides

$8 x + 15 = 0$

$8 x = - 15$

$x = - \frac{15}{8} \mathmr{and} x = - 1 \frac{7}{8}$ (Which are the same things)