2x^4=28x^2-90

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Solution for 2x^4=28x^2-90 equation: 


Simplifying
2x4 = 28x2 + -90

Reorder the terms:
2x4 = -90 + 28x2

Solving
2x4 = -90 + 28x2

Solving for variable 'x'.

Reorder the terms:
90 + -28x2 + 2x4 = -90 + 28x2 + 90 + -28x2

Reorder the terms:
90 + -28x2 + 2x4 = -90 + 90 + 28x2 + -28x2

Combine like terms: -90 + 90 = 0
90 + -28x2 + 2x4 = 0 + 28x2 + -28x2
90 + -28x2 + 2x4 = 28x2 + -28x2

Combine like terms: 28x2 + -28x2 = 0
90 + -28x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + -14x2 + x4) = 0

Factor a trinomial.
2((5 + -1x2)(9 + -1x2)) = 0

Factor a difference between two squares.
2((5 + -1x2)((3 + x)(3 + -1x))) = 0

Ignore the factor 2.

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

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 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 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2.236067978, 2.236067978, -3, 3}

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