x^4-26x^2+120=0

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Solution for x^4-26x^2+120=0 equation:


Simplifying
x4 + -26x2 + 120 = 0

Reorder the terms:
120 + -26x2 + x4 = 0

Solving
120 + -26x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x2)(20 + -1x2) = 0

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 '(20 + -1x2)' equal to zero and attempt to solve: Simplifying 20 + -1x2 = 0 Solving 20 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x2 = 0 + -20 -1x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -1x2 = -20 Divide each side by '-1'. x2 = 20 Simplifying x2 = 20 Take the square root of each side: x = {-4.472135955, 4.472135955}

Solution

x = {-2.449489743, 2.449489743, -4.472135955, 4.472135955}

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