x^4-x^2-10=0

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


Simplifying
x4 + -1x2 + -10 = 0

Reorder the terms:
-10 + -1x2 + x4 = 0

Solving
-10 + -1x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -1x2 + 10 + x4 = 0 + 10

Reorder the terms:
-10 + 10 + -1x2 + x4 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x2 + x4 = 0 + 10
-1x2 + x4 = 0 + 10

Combine like terms: 0 + 10 = 10
-1x2 + x4 = 10

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = 10 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + -1x2 + x4 = 10.25

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x2 + -0.5 = 3.201562119

Simplifying
x2 + -0.5 = 3.201562119

Reorder the terms:
-0.5 + x2 = 3.201562119

Solving
-0.5 + x2 = 3.201562119

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = 3.201562119 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 3.201562119 + 0.5
x2 = 3.201562119 + 0.5

Combine like terms: 3.201562119 + 0.5 = 3.701562119
x2 = 3.701562119

Simplifying
x2 = 3.701562119

Take the square root of each side:
x = {-1.923944417, 1.923944417}


Subproblem 2
x2 + -0.5 = -3.201562119

Simplifying
x2 + -0.5 = -3.201562119

Reorder the terms:
-0.5 + x2 = -3.201562119

Solving
-0.5 + x2 = -3.201562119

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x2 = -3.201562119 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -3.201562119 + 0.5
x2 = -3.201562119 + 0.5

Combine like terms: -3.201562119 + 0.5 = -2.701562119
x2 = -2.701562119

Simplifying
x2 = -2.701562119

Reorder the terms:
2.701562119 + x2 = -2.701562119 + 2.701562119

Combine like terms: -2.701562119 + 2.701562119 = 0.000000000
2.701562119 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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