x^4-30x^2-125=0

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Solution for x^4-30x^2-125=0 equation: 


Simplifying
x4 + -30x2 + -125 = 0

Reorder the terms:
-125 + -30x2 + x4 = 0

Solving
-125 + -30x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + -30x2 + 125 + x4 = 0 + 125

Reorder the terms:
-125 + 125 + -30x2 + x4 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + -30x2 + x4 = 0 + 125
-30x2 + x4 = 0 + 125

Combine like terms: 0 + 125 = 125
-30x2 + x4 = 125

The x term is -30x2.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x2 + 225 + x4 = 125 + 225

Reorder the terms:
225 + -30x2 + x4 = 125 + 225

Combine like terms: 125 + 225 = 350
225 + -30x2 + x4 = 350

Factor a perfect square on the left side:
(x2 + -15)(x2 + -15) = 350

Calculate the square root of the right side: 18.708286934

Break this problem into two subproblems by setting 
(x2 + -15) equal to 18.708286934 and -18.708286934.


Subproblem 1
x2 + -15 = 18.708286934

Simplifying
x2 + -15 = 18.708286934

Reorder the terms:
-15 + x2 = 18.708286934

Solving
-15 + x2 = 18.708286934

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x2 = 18.708286934 + 15

Combine like terms: -15 + 15 = 0
0 + x2 = 18.708286934 + 15
x2 = 18.708286934 + 15

Combine like terms: 18.708286934 + 15 = 33.708286934
x2 = 33.708286934

Simplifying
x2 = 33.708286934

Take the square root of each side:
x = {-5.80588382, 5.80588382}


Subproblem 2
x2 + -15 = -18.708286934

Simplifying
x2 + -15 = -18.708286934

Reorder the terms:
-15 + x2 = -18.708286934

Solving
-15 + x2 = -18.708286934

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x2 = -18.708286934 + 15

Combine like terms: -15 + 15 = 0
0 + x2 = -18.708286934 + 15
x2 = -18.708286934 + 15

Combine like terms: -18.708286934 + 15 = -3.708286934
x2 = -3.708286934

Simplifying
x2 = -3.708286934

Reorder the terms:
3.708286934 + x2 = -3.708286934 + 3.708286934

Combine like terms: -3.708286934 + 3.708286934 = 0.000000000
3.708286934 + x2 = 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.

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