x^4-23x^2-468=0

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Solution for x^4-23x^2-468=0 equation:


Simplifying
x4 + -23x2 + -468 = 0

Reorder the terms:
-468 + -23x2 + x4 = 0

Solving
-468 + -23x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + -1x2)(36 + -1x2) = 0

Factor a difference between two squares.
(-13 + -1x2)((6 + x)(6 + -1x)) = 0

Subproblem 1

Set the factor '(-13 + -1x2)' equal to zero and attempt to solve: Simplifying -13 + -1x2 = 0 Solving -13 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1x2 = 0 + 13 -1x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -1x2 = 13 Divide each side by '-1'. x2 = -13 Simplifying x2 = -13 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Subproblem 3

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-6, 6}

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