x^4-2x^2-64=0

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Solution for x^4-2x^2-64=0 equation:


Simplifying
x4 + -2x2 + -64 = 0

Reorder the terms:
-64 + -2x2 + x4 = 0

Solving
-64 + -2x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -2x2 + 64 + x4 = 0 + 64

Reorder the terms:
-64 + 64 + -2x2 + x4 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -2x2 + x4 = 0 + 64
-2x2 + x4 = 0 + 64

Combine like terms: 0 + 64 = 64
-2x2 + x4 = 64

The x term is -2x2.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x2 + 1 + x4 = 64 + 1

Reorder the terms:
1 + -2x2 + x4 = 64 + 1

Combine like terms: 64 + 1 = 65
1 + -2x2 + x4 = 65

Factor a perfect square on the left side:
(x2 + -1)(x2 + -1) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x2 + -1) equal to 8.062257748 and -8.062257748.

Subproblem 1

x2 + -1 = 8.062257748 Simplifying x2 + -1 = 8.062257748 Reorder the terms: -1 + x2 = 8.062257748 Solving -1 + x2 = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 8.062257748 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 8.062257748 + 1 x2 = 8.062257748 + 1 Combine like terms: 8.062257748 + 1 = 9.062257748 x2 = 9.062257748 Simplifying x2 = 9.062257748 Take the square root of each side: x = {-3.010358409, 3.010358409}

Subproblem 2

x2 + -1 = -8.062257748 Simplifying x2 + -1 = -8.062257748 Reorder the terms: -1 + x2 = -8.062257748 Solving -1 + x2 = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -8.062257748 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -8.062257748 + 1 x2 = -8.062257748 + 1 Combine like terms: -8.062257748 + 1 = -7.062257748 x2 = -7.062257748 Simplifying x2 = -7.062257748 Reorder the terms: 7.062257748 + x2 = -7.062257748 + 7.062257748 Combine like terms: -7.062257748 + 7.062257748 = 0.000000000 7.062257748 + 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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