3x^4+486x^2+7=0

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Solution for 3x^4+486x^2+7=0 equation:


Simplifying
3x4 + 486x2 + 7 = 0

Reorder the terms:
7 + 486x2 + 3x4 = 0

Solving
7 + 486x2 + 3x4 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
2.333333333 + 162x2 + x4 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 162x2 + -2.333333333 + x4 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 162x2 + x4 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 162x2 + x4 = 0 + -2.333333333
162x2 + x4 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
162x2 + x4 = -2.333333333

The x term is 162x2.  Take half its coefficient (81).
Square it (6561) and add it to both sides.

Add '6561' to each side of the equation.
162x2 + 6561 + x4 = -2.333333333 + 6561

Reorder the terms:
6561 + 162x2 + x4 = -2.333333333 + 6561

Combine like terms: -2.333333333 + 6561 = 6558.666666667
6561 + 162x2 + x4 = 6558.666666667

Factor a perfect square on the left side:
(x2 + 81)(x2 + 81) = 6558.666666667

Calculate the square root of the right side: 80.985595427

Break this problem into two subproblems by setting 
(x2 + 81) equal to 80.985595427 and -80.985595427.

Subproblem 1

x2 + 81 = 80.985595427 Simplifying x2 + 81 = 80.985595427 Reorder the terms: 81 + x2 = 80.985595427 Solving 81 + x2 = 80.985595427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-81' to each side of the equation. 81 + -81 + x2 = 80.985595427 + -81 Combine like terms: 81 + -81 = 0 0 + x2 = 80.985595427 + -81 x2 = 80.985595427 + -81 Combine like terms: 80.985595427 + -81 = -0.014404573 x2 = -0.014404573 Simplifying x2 = -0.014404573 Reorder the terms: 0.014404573 + x2 = -0.014404573 + 0.014404573 Combine like terms: -0.014404573 + 0.014404573 = 0.000000000 0.014404573 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

x2 + 81 = -80.985595427 Simplifying x2 + 81 = -80.985595427 Reorder the terms: 81 + x2 = -80.985595427 Solving 81 + x2 = -80.985595427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-81' to each side of the equation. 81 + -81 + x2 = -80.985595427 + -81 Combine like terms: 81 + -81 = 0 0 + x2 = -80.985595427 + -81 x2 = -80.985595427 + -81 Combine like terms: -80.985595427 + -81 = -161.985595427 x2 = -161.985595427 Simplifying x2 = -161.985595427 Reorder the terms: 161.985595427 + x2 = -161.985595427 + 161.985595427 Combine like terms: -161.985595427 + 161.985595427 = 0.000000000 161.985595427 + 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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