x^4+0.5x^2+0.0625=0

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Solution for x^4+0.5x^2+0.0625=0 equation:


Simplifying
x4 + 0.5x2 + 0.0625 = 0

Reorder the terms:
0.0625 + 0.5x2 + x4 = 0

Solving
0.0625 + 0.5x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + 0.5x2 + -0.0625 + x4 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + 0.5x2 + x4 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + 0.5x2 + x4 = 0 + -0.0625
0.5x2 + x4 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
0.5x2 + x4 = -0.0625

The x term is 0.5x2.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x2 + 0.0625 + x4 = -0.0625 + 0.0625

Reorder the terms:
0.0625 + 0.5x2 + x4 = -0.0625 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0625 + 0.5x2 + x4 = 0.0000

Factor a perfect square on the left side:
(x2 + 0.25)(x2 + 0.25) = 0.0000

Calculate the square root of the right side: 0.0000

Break this problem into two subproblems by setting 
(x2 + 0.25) equal to 0.0000 and 0.0000.

Subproblem 1

x2 + 0.25 = 0.0000 Simplifying x2 + 0.25 = 0.0000 Reorder the terms: 0.25 + x2 = 0.0000 Solving 0.25 + x2 = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = 0.0000 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 0.0000 + -0.25 x2 = 0.0000 + -0.25 Combine like terms: 0.0000 + -0.25 = -0.25 x2 = -0.25 Simplifying x2 = -0.25 Reorder the terms: 0.25 + x2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + x2 = 0.00 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

x2 + 0.25 = 0.0000 Simplifying x2 + 0.25 = 0.0000 Reorder the terms: 0.25 + x2 = 0.0000 Solving 0.25 + x2 = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = 0.0000 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 0.0000 + -0.25 x2 = 0.0000 + -0.25 Combine like terms: 0.0000 + -0.25 = -0.25 x2 = -0.25 Simplifying x2 = -0.25 Reorder the terms: 0.25 + x2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + x2 = 0.00 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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