4x^4-63x^2-4=0

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Solution for 4x^4-63x^2-4=0 equation:


Simplifying
4x4 + -63x2 + -4 = 0

Reorder the terms:
-4 + -63x2 + 4x4 = 0

Solving
-4 + -63x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1 + -15.75x2 + x4 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -15.75x2 + 1 + x4 = 0 + 1

Reorder the terms:
-1 + 1 + -15.75x2 + x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -15.75x2 + x4 = 0 + 1
-15.75x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
-15.75x2 + x4 = 1

The x term is -15.75x2.  Take half its coefficient (-7.875).
Square it (62.015625) and add it to both sides.

Add '62.015625' to each side of the equation.
-15.75x2 + 62.015625 + x4 = 1 + 62.015625

Reorder the terms:
62.015625 + -15.75x2 + x4 = 1 + 62.015625

Combine like terms: 1 + 62.015625 = 63.015625
62.015625 + -15.75x2 + x4 = 63.015625

Factor a perfect square on the left side:
(x2 + -7.875)(x2 + -7.875) = 63.015625

Calculate the square root of the right side: 7.938238155

Break this problem into two subproblems by setting 
(x2 + -7.875) equal to 7.938238155 and -7.938238155.

Subproblem 1

x2 + -7.875 = 7.938238155 Simplifying x2 + -7.875 = 7.938238155 Reorder the terms: -7.875 + x2 = 7.938238155 Solving -7.875 + x2 = 7.938238155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.875' to each side of the equation. -7.875 + 7.875 + x2 = 7.938238155 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + x2 = 7.938238155 + 7.875 x2 = 7.938238155 + 7.875 Combine like terms: 7.938238155 + 7.875 = 15.813238155 x2 = 15.813238155 Simplifying x2 = 15.813238155 Take the square root of each side: x = {-3.976586244, 3.976586244}

Subproblem 2

x2 + -7.875 = -7.938238155 Simplifying x2 + -7.875 = -7.938238155 Reorder the terms: -7.875 + x2 = -7.938238155 Solving -7.875 + x2 = -7.938238155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.875' to each side of the equation. -7.875 + 7.875 + x2 = -7.938238155 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + x2 = -7.938238155 + 7.875 x2 = -7.938238155 + 7.875 Combine like terms: -7.938238155 + 7.875 = -0.063238155 x2 = -0.063238155 Simplifying x2 = -0.063238155 Reorder the terms: 0.063238155 + x2 = -0.063238155 + 0.063238155 Combine like terms: -0.063238155 + 0.063238155 = 0.000000000 0.063238155 + 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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