x^4-56x^2+640=0

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Solution for x^4-56x^2+640=0 equation: 


Simplifying
x4 + -56x2 + 640 = 0

Reorder the terms:
640 + -56x2 + x4 = 0

Solving
640 + -56x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(16 + -1x2)(40 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(40 + -1x2) = 0


Subproblem 1
Set the factor '(40 + -1x2)' equal to zero and attempt to solve:

Simplifying
40 + -1x2 = 0

Solving
40 + -1x2 = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1x2 = 0 + -40
-1x2 = 0 + -40

Combine like terms: 0 + -40 = -40
-1x2 = -40

Divide each side by '-1'.
x2 = 40

Simplifying
x2 = 40

Take the square root of each side:
x = {-6.32455532, 6.32455532}

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6.32455532, 6.32455532, -4, 4}

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