10x^4+-66x^2+56=0

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Solution for 10x^4+-66x^2+56=0 equation: 


Simplifying
10x4 + -66x2 + 56 = 0

Reorder the terms:
56 + -66x2 + 10x4 = 0

Solving
56 + -66x2 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -33x2 + 5x4) = 0

Factor a trinomial.
2((1 + -1x2)(28 + -5x2)) = 0

Factor a difference between two squares.
2(((1 + x)(1 + -1x))(28 + -5x2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(28 + -5x2)' equal to zero and attempt to solve:

Simplifying
28 + -5x2 = 0

Solving
28 + -5x2 = 0

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

Add '-28' to each side of the equation.
28 + -28 + -5x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -5x2 = 0 + -28
-5x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-5x2 = -28

Divide each side by '-5'.
x2 = 5.6

Simplifying
x2 = 5.6

Take the square root of each side:
x = {-2.366431913, 2.366431913}

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.366431913, 2.366431913, -1, 1}

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