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Simplifying x4 + 9x2 + -52 = 0 Reorder the terms: -52 + 9x2 + x4 = 0 Solving -52 + 9x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (-13 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. (-13 + -1x2)((2 + x)(2 + -1x)) = 0Subproblem 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-2, 2}
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