=X^4+7X^2-8

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Solution for =X^4+7X^2-8 equation: 


Simplifying
0 = X4 + 7X2 + -8

Reorder the terms:
0 = -8 + 7X2 + X4

Solving
0 = -8 + 7X2 + X4

Solving for variable 'X'.

Combine like terms: 0 + 8 = 8
8 + -7X2 + -1X4 = -8 + 7X2 + X4 + 8 + -7X2 + -1X4

Reorder the terms:
8 + -7X2 + -1X4 = -8 + 8 + 7X2 + -7X2 + X4 + -1X4

Combine like terms: -8 + 8 = 0
8 + -7X2 + -1X4 = 0 + 7X2 + -7X2 + X4 + -1X4
8 + -7X2 + -1X4 = 7X2 + -7X2 + X4 + -1X4

Combine like terms: 7X2 + -7X2 = 0
8 + -7X2 + -1X4 = 0 + X4 + -1X4
8 + -7X2 + -1X4 = X4 + -1X4

Combine like terms: X4 + -1X4 = 0
8 + -7X2 + -1X4 = 0

Factor a trinomial.
(1 + -1X2)(8 + X2) = 0

Factor a difference between two squares.
((1 + X)(1 + -1X))(8 + X2) = 0


Subproblem 1
Set the factor '(8 + X2)' equal to zero and attempt to solve:

Simplifying
8 + X2 = 0

Solving
8 + X2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + X2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + X2 = 0 + -8
X2 = 0 + -8

Combine like terms: 0 + -8 = -8
X2 = -8

Simplifying
X2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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 = {-1, 1}

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