First, add color(red)(2) to each side of the equation to isolate the x^2 term while keeping the equation balanced:
-3/5x^2 - 2 + color(red)(2) = -5 + color(red)(2)
-3/5x^2 - 0 = -3
-3/5x^2 = -3
Next, multiply each side of the equation by -color(red)(5)/color(blue)(3) to isolate x^2 while keeping the equation balanced:
-color(red)(5)/color(blue)(3) xx -3/5x^2 = -color(red)(5)/color(blue)(3) xx -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) = +-sqrt(5)
x = +-sqrt(5) = +-2.236 rounded to the nearest thousandth
