# How do you solve the equation -3/5x^2-2=-5?

Feb 13, 2017

See the entire solution process below:

#### Explanation:

First, add $\textcolor{red}{2}$ to each side of the equation to isolate the ${x}^{2}$ term while keeping the equation balanced:

$- \frac{3}{5} {x}^{2} - 2 + \textcolor{red}{2} = - 5 + \textcolor{red}{2}$

$- \frac{3}{5} {x}^{2} - 0 = - 3$

$- \frac{3}{5} {x}^{2} = - 3$

Next, multiply each side of the equation by $- \frac{\textcolor{red}{5}}{\textcolor{b l u e}{3}}$ to isolate ${x}^{2}$ while keeping the equation balanced:

$- \frac{\textcolor{red}{5}}{\textcolor{b l u e}{3}} \times - \frac{3}{5} {x}^{2} = - \frac{\textcolor{red}{5}}{\textcolor{b l u e}{3}} \times - 3$

cancel(color(red)(-5))/cancel(color(blue)(3)) xx color(blue)(cancel(color(black)(-3)))/color(red)(cancel(color(black)(5)))x^2 = -color(red)(5)/cancel(color(blue)(3)) xx -cancel(color(blue)(3)

${x}^{2} = 5$

Now, take the square root of each side of the equation to solve for $x$ while keeping the equation balanced. Remember, when taking the square root of the number there is a positive and negative solution.

$\sqrt{{x}^{2}} = \pm \sqrt{5}$

$x = \pm \sqrt{5} = \pm 2.236$ rounded to the nearest thousandth