x^4-24x^2+80=0

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Solution for x^4-24x^2+80=0 equation: 


Simplifying
x4 + -24x2 + 80 = 0

Reorder the terms:
80 + -24x2 + x4 = 0

Solving
80 + -24x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(20 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(20 + -1x2) = 0


Subproblem 1
Set the factor '(20 + -1x2)' equal to zero and attempt to solve:

Simplifying
20 + -1x2 = 0

Solving
20 + -1x2 = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x2 = 0 + -20
-1x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-1x2 = -20

Divide each side by '-1'.
x2 = 20

Simplifying
x2 = 20

Take the square root of each side:
x = {-4.472135955, 4.472135955}

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 = {-4.472135955, 4.472135955, -2, 2}

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