2x^4-8x^2+5=-5+5x^2-2x^4

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Solution for 2x^4-8x^2+5=-5+5x^2-2x^4 equation: 


Simplifying
2x4 + -8x2 + 5 = -5 + 5x2 + -2x4

Reorder the terms:
5 + -8x2 + 2x4 = -5 + 5x2 + -2x4

Solving
5 + -8x2 + 2x4 = -5 + 5x2 + -2x4

Solving for variable 'x'.

Reorder the terms:
5 + 5 + -8x2 + -5x2 + 2x4 + 2x4 = -5 + 5x2 + -2x4 + 5 + -5x2 + 2x4

Combine like terms: 5 + 5 = 10
10 + -8x2 + -5x2 + 2x4 + 2x4 = -5 + 5x2 + -2x4 + 5 + -5x2 + 2x4

Combine like terms: -8x2 + -5x2 = -13x2
10 + -13x2 + 2x4 + 2x4 = -5 + 5x2 + -2x4 + 5 + -5x2 + 2x4

Combine like terms: 2x4 + 2x4 = 4x4
10 + -13x2 + 4x4 = -5 + 5x2 + -2x4 + 5 + -5x2 + 2x4

Reorder the terms:
10 + -13x2 + 4x4 = -5 + 5 + 5x2 + -5x2 + -2x4 + 2x4

Combine like terms: -5 + 5 = 0
10 + -13x2 + 4x4 = 0 + 5x2 + -5x2 + -2x4 + 2x4
10 + -13x2 + 4x4 = 5x2 + -5x2 + -2x4 + 2x4

Combine like terms: 5x2 + -5x2 = 0
10 + -13x2 + 4x4 = 0 + -2x4 + 2x4
10 + -13x2 + 4x4 = -2x4 + 2x4

Combine like terms: -2x4 + 2x4 = 0
10 + -13x2 + 4x4 = 0

Factor a trinomial.
(5 + -4x2)(2 + -1x2) = 0


Subproblem 1
Set the factor '(5 + -4x2)' equal to zero and attempt to solve:

Simplifying
5 + -4x2 = 0

Solving
5 + -4x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x2 = 0 + -5
-4x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-4x2 = -5

Divide each side by '-4'.
x2 = 1.25

Simplifying
x2 = 1.25

Take the square root of each side:
x = {-1.118033989, 1.118033989}

Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {-1.118033989, 1.118033989, -1.414213562, 1.414213562}

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