x^4-5x^2=5x^2-25

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Solution for x^4-5x^2=5x^2-25 equation: 


Simplifying
x4 + -5x2 = 5x2 + -25

Reorder the terms:
-5x2 + x4 = 5x2 + -25

Reorder the terms:
-5x2 + x4 = -25 + 5x2

Solving
-5x2 + x4 = -25 + 5x2

Solving for variable 'x'.

Reorder the terms:
25 + -5x2 + -5x2 + x4 = -25 + 5x2 + 25 + -5x2

Combine like terms: -5x2 + -5x2 = -10x2
25 + -10x2 + x4 = -25 + 5x2 + 25 + -5x2

Reorder the terms:
25 + -10x2 + x4 = -25 + 25 + 5x2 + -5x2

Combine like terms: -25 + 25 = 0
25 + -10x2 + x4 = 0 + 5x2 + -5x2
25 + -10x2 + x4 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
25 + -10x2 + x4 = 0

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


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 '(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}
Solution
x = {-2.236067978, 2.236067978, -2.236067978, 2.236067978}

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