2x^4-9x^2=2

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Solution for 2x^4-9x^2=2 equation:


Simplifying
2x4 + -9x2 = 2

Reorder the terms:
-9x2 + 2x4 = 2

Solving
-9x2 + 2x4 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -9x2 + 2x4 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -9x2 + 2x4 = 0

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

Divide each side by '2'.
-1 + -4.5x2 + x4 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.5x2 + 1 + x4 = 0 + 1

Reorder the terms:
-1 + 1 + -4.5x2 + x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.5x2 + x4 = 0 + 1
-4.5x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.5x2 + x4 = 1

The x term is -4.5x2.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x2 + 5.0625 + x4 = 1 + 5.0625

Reorder the terms:
5.0625 + -4.5x2 + x4 = 1 + 5.0625

Combine like terms: 1 + 5.0625 = 6.0625
5.0625 + -4.5x2 + x4 = 6.0625

Factor a perfect square on the left side:
(x2 + -2.25)(x2 + -2.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x2 + -2.25) equal to 2.46221445 and -2.46221445.

Subproblem 1

x2 + -2.25 = 2.46221445 Simplifying x2 + -2.25 = 2.46221445 Reorder the terms: -2.25 + x2 = 2.46221445 Solving -2.25 + x2 = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x2 = 2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x2 = 2.46221445 + 2.25 x2 = 2.46221445 + 2.25 Combine like terms: 2.46221445 + 2.25 = 4.71221445 x2 = 4.71221445 Simplifying x2 = 4.71221445 Take the square root of each side: x = {-2.170763564, 2.170763564}

Subproblem 2

x2 + -2.25 = -2.46221445 Simplifying x2 + -2.25 = -2.46221445 Reorder the terms: -2.25 + x2 = -2.46221445 Solving -2.25 + x2 = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x2 = -2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x2 = -2.46221445 + 2.25 x2 = -2.46221445 + 2.25 Combine like terms: -2.46221445 + 2.25 = -0.21221445 x2 = -0.21221445 Simplifying x2 = -0.21221445 Reorder the terms: 0.21221445 + x2 = -0.21221445 + 0.21221445 Combine like terms: -0.21221445 + 0.21221445 = 0.00000000 0.21221445 + x2 = 0.00000000 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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