r^2=2(r^2-50)

Solution for r^2=2(r^2-50) equation:

Simplifying
r2 = 2(r2 + -50)

Reorder the terms:
r2 = 2(-50 + r2)
r2 = (-50 * 2 + r2 * 2)
r2 = (-100 + 2r2)

Solving
r2 = -100 + 2r2

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-2r2' to each side of the equation.
r2 + -2r2 = -100 + 2r2 + -2r2

Combine like terms: r2 + -2r2 = -1r2
-1r2 = -100 + 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
-1r2 = -100 + 0
-1r2 = -100

Divide each side by '-1'.
r2 = 100

Simplifying
r2 = 100

Take the square root of each side:
r = {-10, 10}