2x^2=x^4-2x^2

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Solution for 2x^2=x^4-2x^2 equation: 


Simplifying
2x2 = x4 + -2x2

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

Solving
2x2 = -2x2 + x4

Solving for variable 'x'.

Combine like terms: 2x2 + 2x2 = 4x2
4x2 + -1x4 = -2x2 + x4 + 2x2 + -1x4

Reorder the terms:
4x2 + -1x4 = -2x2 + 2x2 + x4 + -1x4

Combine like terms: -2x2 + 2x2 = 0
4x2 + -1x4 = 0 + x4 + -1x4
4x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
4x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4 + -1x2) = 0

Factor a difference between two squares.
x2((2 + x)(2 + -1x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

Simplifying
x = 2
Solution
x = {0, -2, 2}

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