# How do you solve the equation 1/3(x+4)^2-1=5?

Mar 12, 2017

$3 \setminus \sqrt{2} - 4$

#### Explanation:

new/changed values are in \color(indianred)(\text{this }color)

$\frac{1}{3} {\left(x + 4\right)}^{2} - 1 = 5$
add 1 to both sides (cancels out the $- 1$)...
$\frac{1}{3} {\left(x + 4\right)}^{2} = \setminus \textcolor{\in \mathrm{di} a n red}{6}$
multiply both sides by 3 (cancels out the $\frac{1}{3}$)...
${\left(x + 4\right)}^{2} = \setminus \textcolor{\in \mathrm{di} a n red}{18}$
square root both sides (cancels out square on left)...
$x + 4 = \setminus \textcolor{\in \mathrm{di} a n red}{\setminus \sqrt{18}}$
subtract 4 from both sides (cancels out the $- 4$)...
$x = \setminus \sqrt{18} \setminus \textcolor{\in \mathrm{di} a n red}{- 4}$

now we have the base result, $x = \setminus \sqrt{18} - 4$
but this can be simplified...
$\setminus \sqrt{18} = \setminus \sqrt{\setminus \cancel{3} \setminus \cdot \setminus \cancel{3} \setminus \cdot 2} = 3 \setminus \sqrt{2}$
therefore, your result is...