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

1 Answer
Feb 13, 2017

Answer:

See the entire solution process below:

Explanation:

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