x^4+8x^2-30=0

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Solution for x^4+8x^2-30=0 equation: 


Simplifying
x4 + 8x2 + -30 = 0

Reorder the terms:
-30 + 8x2 + x4 = 0

Solving
-30 + 8x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 8x2 + 30 + x4 = 0 + 30

Reorder the terms:
-30 + 30 + 8x2 + x4 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 8x2 + x4 = 0 + 30
8x2 + x4 = 0 + 30

Combine like terms: 0 + 30 = 30
8x2 + x4 = 30

The x term is 8x2.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x2 + 16 + x4 = 30 + 16

Reorder the terms:
16 + 8x2 + x4 = 30 + 16

Combine like terms: 30 + 16 = 46
16 + 8x2 + x4 = 46

Factor a perfect square on the left side:
(x2 + 4)(x2 + 4) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x2 + 4) equal to 6.782329983 and -6.782329983.


Subproblem 1
x2 + 4 = 6.782329983

Simplifying
x2 + 4 = 6.782329983

Reorder the terms:
4 + x2 = 6.782329983

Solving
4 + x2 = 6.782329983

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x2 = 6.782329983 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = 6.782329983 + -4
x2 = 6.782329983 + -4

Combine like terms: 6.782329983 + -4 = 2.782329983
x2 = 2.782329983

Simplifying
x2 = 2.782329983

Take the square root of each side:
x = {-1.668031769, 1.668031769}


Subproblem 2
x2 + 4 = -6.782329983

Simplifying
x2 + 4 = -6.782329983

Reorder the terms:
4 + x2 = -6.782329983

Solving
4 + x2 = -6.782329983

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x2 = -6.782329983 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = -6.782329983 + -4
x2 = -6.782329983 + -4

Combine like terms: -6.782329983 + -4 = -10.782329983
x2 = -10.782329983

Simplifying
x2 = -10.782329983

Reorder the terms:
10.782329983 + x2 = -10.782329983 + 10.782329983

Combine like terms: -10.782329983 + 10.782329983 = 0.000000000
10.782329983 + 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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