18x^4-5x^2=2

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Solution for 18x^4-5x^2=2 equation:


Simplifying
18x4 + -5x2 = 2

Reorder the terms:
-5x2 + 18x4 = 2

Solving
-5x2 + 18x4 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -5x2 + 18x4 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -5x2 + 18x4 = 0

Factor a trinomial.
(-2 + -9x2)(1 + -2x2) = 0

Subproblem 1

Set the factor '(-2 + -9x2)' equal to zero and attempt to solve: Simplifying -2 + -9x2 = 0 Solving -2 + -9x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -9x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -9x2 = 0 + 2 -9x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -9x2 = 2 Divide each side by '-9'. x2 = -0.2222222222 Simplifying x2 = -0.2222222222 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -2x2 = 0 Solving 1 + -2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x2 = 0 + -1 -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2x2 = -1 Divide each side by '-2'. x2 = 0.5 Simplifying x2 = 0.5 Take the square root of each side: x = {-0.707106781, 0.707106781}

Solution

x = {-0.707106781, 0.707106781}

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