x^4=29x^2-100

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Solution for x^4=29x^2-100 equation: 


Simplifying
x4 = 29x2 + -100

Reorder the terms:
x4 = -100 + 29x2

Solving
x4 = -100 + 29x2

Solving for variable 'x'.

Reorder the terms:
100 + -29x2 + x4 = -100 + 29x2 + 100 + -29x2

Reorder the terms:
100 + -29x2 + x4 = -100 + 100 + 29x2 + -29x2

Combine like terms: -100 + 100 = 0
100 + -29x2 + x4 = 0 + 29x2 + -29x2
100 + -29x2 + x4 = 29x2 + -29x2

Combine like terms: 29x2 + -29x2 = 0
100 + -29x2 + x4 = 0

Factor a trinomial.
(4 + -1x2)(25 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(25 + -1x2) = 0

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


Subproblem 1
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 2
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

Subproblem 3
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

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

Simplifying
x = 5
Solution
x = {-2, 2, -5, 5}

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