r^4-50r^2-625=0

Solution for r^4-50r^2-625=0 equation:

Simplifying
r4 + -50r2 + -625 = 0

Reorder the terms:
-625 + -50r2 + r4 = 0

Solving
-625 + -50r2 + r4 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '625' to each side of the equation.
-625 + -50r2 + 625 + r4 = 0 + 625

Reorder the terms:
-625 + 625 + -50r2 + r4 = 0 + 625

Combine like terms: -625 + 625 = 0
0 + -50r2 + r4 = 0 + 625
-50r2 + r4 = 0 + 625

Combine like terms: 0 + 625 = 625
-50r2 + r4 = 625

The r term is -50r2.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50r2 + 625 + r4 = 625 + 625

Reorder the terms:
625 + -50r2 + r4 = 625 + 625

Combine like terms: 625 + 625 = 1250
625 + -50r2 + r4 = 1250

Factor a perfect square on the left side:
(r2 + -25)(r2 + -25) = 1250

Calculate the square root of the right side: 35.355339059

Break this problem into two subproblems by setting 
(r2 + -25) equal to 35.355339059 and -35.355339059.

Subproblem 1
r2 + -25 = 35.355339059

Simplifying
r2 + -25 = 35.355339059

Reorder the terms:
-25 + r2 = 35.355339059

Solving
-25 + r2 = 35.355339059

Solving for variable 'r'.

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

Add '25' to each side of the equation.
-25 + 25 + r2 = 35.355339059 + 25

Combine like terms: -25 + 25 = 0
0 + r2 = 35.355339059 + 25
r2 = 35.355339059 + 25

Combine like terms: 35.355339059 + 25 = 60.355339059
r2 = 60.355339059

Simplifying
r2 = 60.355339059

Take the square root of each side:
r = {-7.76886987, 7.76886987}

Subproblem 2
r2 + -25 = -35.355339059

Simplifying
r2 + -25 = -35.355339059

Reorder the terms:
-25 + r2 = -35.355339059

Solving
-25 + r2 = -35.355339059

Solving for variable 'r'.

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

Add '25' to each side of the equation.
-25 + 25 + r2 = -35.355339059 + 25

Combine like terms: -25 + 25 = 0
0 + r2 = -35.355339059 + 25
r2 = -35.355339059 + 25

Combine like terms: -35.355339059 + 25 = -10.355339059
r2 = -10.355339059

Simplifying
r2 = -10.355339059

Reorder the terms:
10.355339059 + r2 = -10.355339059 + 10.355339059

Combine like terms: -10.355339059 + 10.355339059 = 0.000000000
10.355339059 + r2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.