x^4+15x^2-16=-2

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Solution for x^4+15x^2-16=-2 equation: 


Simplifying
x4 + 15x2 + -16 = -2

Reorder the terms:
-16 + 15x2 + x4 = -2

Solving
-16 + 15x2 + x4 = -2

Solving for variable 'x'.

Reorder the terms:
-16 + 2 + 15x2 + x4 = -2 + 2

Combine like terms: -16 + 2 = -14
-14 + 15x2 + x4 = -2 + 2

Combine like terms: -2 + 2 = 0
-14 + 15x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 15x2 + 14 + x4 = 0 + 14

Reorder the terms:
-14 + 14 + 15x2 + x4 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 15x2 + x4 = 0 + 14
15x2 + x4 = 0 + 14

Combine like terms: 0 + 14 = 14
15x2 + x4 = 14

The x term is 15x2.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x2 + 56.25 + x4 = 14 + 56.25

Reorder the terms:
56.25 + 15x2 + x4 = 14 + 56.25

Combine like terms: 14 + 56.25 = 70.25
56.25 + 15x2 + x4 = 70.25

Factor a perfect square on the left side:
(x2 + 7.5)(x2 + 7.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x2 + 7.5) equal to 8.381527307 and -8.381527307.


Subproblem 1
x2 + 7.5 = 8.381527307

Simplifying
x2 + 7.5 = 8.381527307

Reorder the terms:
7.5 + x2 = 8.381527307

Solving
7.5 + x2 = 8.381527307

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x2 = 8.381527307 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x2 = 8.381527307 + -7.5
x2 = 8.381527307 + -7.5

Combine like terms: 8.381527307 + -7.5 = 0.881527307
x2 = 0.881527307

Simplifying
x2 = 0.881527307

Take the square root of each side:
x = {-0.938896856, 0.938896856}


Subproblem 2
x2 + 7.5 = -8.381527307

Simplifying
x2 + 7.5 = -8.381527307

Reorder the terms:
7.5 + x2 = -8.381527307

Solving
7.5 + x2 = -8.381527307

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x2 = -8.381527307 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x2 = -8.381527307 + -7.5
x2 = -8.381527307 + -7.5

Combine like terms: -8.381527307 + -7.5 = -15.881527307
x2 = -15.881527307

Simplifying
x2 = -15.881527307

Reorder the terms:
15.881527307 + x2 = -15.881527307 + 15.881527307

Combine like terms: -15.881527307 + 15.881527307 = 0.000000000
15.881527307 + 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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