2x^4-24x^2+72=0

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Solution for 2x^4-24x^2+72=0 equation:


Simplifying
2x4 + -24x2 + 72 = 0

Reorder the terms:
72 + -24x2 + 2x4 = 0

Solving
72 + -24x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -12x2 + x4) = 0

Factor a trinomial.
2((6 + -1x2)(6 + -1x2)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(6 + -1x2)' equal to zero and attempt to solve: Simplifying 6 + -1x2 = 0 Solving 6 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x2 = 0 + -6 -1x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1x2 = -6 Divide each side by '-1'. x2 = 6 Simplifying x2 = 6 Take the square root of each side: x = {-2.449489743, 2.449489743}

Subproblem 2

Set the factor '(6 + -1x2)' equal to zero and attempt to solve: Simplifying 6 + -1x2 = 0 Solving 6 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x2 = 0 + -6 -1x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1x2 = -6 Divide each side by '-1'. x2 = 6 Simplifying x2 = 6 Take the square root of each side: x = {-2.449489743, 2.449489743}

Solution

x = {-2.449489743, 2.449489743, -2.449489743, 2.449489743}

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