x^4+64x^2-1024=0

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Solution for x^4+64x^2-1024=0 equation:


Simplifying
x4 + 64x2 + -1024 = 0

Reorder the terms:
-1024 + 64x2 + x4 = 0

Solving
-1024 + 64x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1024' to each side of the equation.
-1024 + 64x2 + 1024 + x4 = 0 + 1024

Reorder the terms:
-1024 + 1024 + 64x2 + x4 = 0 + 1024

Combine like terms: -1024 + 1024 = 0
0 + 64x2 + x4 = 0 + 1024
64x2 + x4 = 0 + 1024

Combine like terms: 0 + 1024 = 1024
64x2 + x4 = 1024

The x term is 64x2.  Take half its coefficient (32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
64x2 + 1024 + x4 = 1024 + 1024

Reorder the terms:
1024 + 64x2 + x4 = 1024 + 1024

Combine like terms: 1024 + 1024 = 2048
1024 + 64x2 + x4 = 2048

Factor a perfect square on the left side:
(x2 + 32)(x2 + 32) = 2048

Calculate the square root of the right side: 45.254833996

Break this problem into two subproblems by setting 
(x2 + 32) equal to 45.254833996 and -45.254833996.

Subproblem 1

x2 + 32 = 45.254833996 Simplifying x2 + 32 = 45.254833996 Reorder the terms: 32 + x2 = 45.254833996 Solving 32 + x2 = 45.254833996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x2 = 45.254833996 + -32 Combine like terms: 32 + -32 = 0 0 + x2 = 45.254833996 + -32 x2 = 45.254833996 + -32 Combine like terms: 45.254833996 + -32 = 13.254833996 x2 = 13.254833996 Simplifying x2 = 13.254833996 Take the square root of each side: x = {-3.640718885, 3.640718885}

Subproblem 2

x2 + 32 = -45.254833996 Simplifying x2 + 32 = -45.254833996 Reorder the terms: 32 + x2 = -45.254833996 Solving 32 + x2 = -45.254833996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x2 = -45.254833996 + -32 Combine like terms: 32 + -32 = 0 0 + x2 = -45.254833996 + -32 x2 = -45.254833996 + -32 Combine like terms: -45.254833996 + -32 = -77.254833996 x2 = -77.254833996 Simplifying x2 = -77.254833996 Reorder the terms: 77.254833996 + x2 = -77.254833996 + 77.254833996 Combine like terms: -77.254833996 + 77.254833996 = 0.000000000 77.254833996 + 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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