2x^4-28x^2-90=0

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Solution for 2x^4-28x^2-90=0 equation:


Simplifying
2x4 + -28x2 + -90 = 0

Reorder the terms:
-90 + -28x2 + 2x4 = 0

Solving
-90 + -28x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -14x2 + x4) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-45 + -14x2 + x4)' equal to zero and attempt to solve: Simplifying -45 + -14x2 + x4 = 0 Solving -45 + -14x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -14x2 + 45 + x4 = 0 + 45 Reorder the terms: -45 + 45 + -14x2 + x4 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -14x2 + x4 = 0 + 45 -14x2 + x4 = 0 + 45 Combine like terms: 0 + 45 = 45 -14x2 + x4 = 45 The x term is -14x2. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x2 + 49 + x4 = 45 + 49 Reorder the terms: 49 + -14x2 + x4 = 45 + 49 Combine like terms: 45 + 49 = 94 49 + -14x2 + x4 = 94 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x2 + -7) equal to 9.695359715 and -9.695359715.

Subproblem 1

x2 + -7 = 9.695359715 Simplifying x2 + -7 = 9.695359715 Reorder the terms: -7 + x2 = 9.695359715 Solving -7 + x2 = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 9.695359715 + 7 x2 = 9.695359715 + 7 Combine like terms: 9.695359715 + 7 = 16.695359715 x2 = 16.695359715 Simplifying x2 = 16.695359715 Take the square root of each side: x = {-4.08599556, 4.08599556}

Subproblem 2

x2 + -7 = -9.695359715 Simplifying x2 + -7 = -9.695359715 Reorder the terms: -7 + x2 = -9.695359715 Solving -7 + x2 = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -9.695359715 + 7 x2 = -9.695359715 + 7 Combine like terms: -9.695359715 + 7 = -2.695359715 x2 = -2.695359715 Simplifying x2 = -2.695359715 Reorder the terms: 2.695359715 + x2 = -2.695359715 + 2.695359715 Combine like terms: -2.695359715 + 2.695359715 = 0.000000000 2.695359715 + 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. 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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