0=x^4-17x^2-16

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Solution for 0=x^4-17x^2-16 equation: 


Simplifying
0 = x4 + -17x2 + -16

Reorder the terms:
0 = -16 + -17x2 + x4

Solving
0 = -16 + -17x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 16 = 16
16 + 17x2 + -1x4 = -16 + -17x2 + x4 + 16 + 17x2 + -1x4

Reorder the terms:
16 + 17x2 + -1x4 = -16 + 16 + -17x2 + 17x2 + x4 + -1x4

Combine like terms: -16 + 16 = 0
16 + 17x2 + -1x4 = 0 + -17x2 + 17x2 + x4 + -1x4
16 + 17x2 + -1x4 = -17x2 + 17x2 + x4 + -1x4

Combine like terms: -17x2 + 17x2 = 0
16 + 17x2 + -1x4 = 0 + x4 + -1x4
16 + 17x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
16 + 17x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + -17x2 + x4 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -17x2 + 16 + x4 = 0 + 16

Reorder the terms:
-16 + 16 + -17x2 + x4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -17x2 + x4 = 0 + 16
-17x2 + x4 = 0 + 16

Combine like terms: 0 + 16 = 16
-17x2 + x4 = 16

The x term is -17x2.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x2 + 72.25 + x4 = 16 + 72.25

Reorder the terms:
72.25 + -17x2 + x4 = 16 + 72.25

Combine like terms: 16 + 72.25 = 88.25
72.25 + -17x2 + x4 = 88.25

Factor a perfect square on the left side:
(x2 + -8.5)(x2 + -8.5) = 88.25

Calculate the square root of the right side: 9.394147114

Break this problem into two subproblems by setting 
(x2 + -8.5) equal to 9.394147114 and -9.394147114.


Subproblem 1
x2 + -8.5 = 9.394147114

Simplifying
x2 + -8.5 = 9.394147114

Reorder the terms:
-8.5 + x2 = 9.394147114

Solving
-8.5 + x2 = 9.394147114

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x2 = 9.394147114 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x2 = 9.394147114 + 8.5
x2 = 9.394147114 + 8.5

Combine like terms: 9.394147114 + 8.5 = 17.894147114
x2 = 17.894147114

Simplifying
x2 = 17.894147114

Take the square root of each side:
x = {-4.23014741, 4.23014741}


Subproblem 2
x2 + -8.5 = -9.394147114

Simplifying
x2 + -8.5 = -9.394147114

Reorder the terms:
-8.5 + x2 = -9.394147114

Solving
-8.5 + x2 = -9.394147114

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x2 = -9.394147114 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x2 = -9.394147114 + 8.5
x2 = -9.394147114 + 8.5

Combine like terms: -9.394147114 + 8.5 = -0.894147114
x2 = -0.894147114

Simplifying
x2 = -0.894147114

Reorder the terms:
0.894147114 + x2 = -0.894147114 + 0.894147114

Combine like terms: -0.894147114 + 0.894147114 = 0.000000000
0.894147114 + 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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