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Simplifying 4x4 = 24x2 + 108 Reorder the terms: 4x4 = 108 + 24x2 Solving 4x4 = 108 + 24x2 Solving for variable 'x'. Reorder the terms: -108 + -24x2 + 4x4 = 108 + 24x2 + -108 + -24x2 Reorder the terms: -108 + -24x2 + 4x4 = 108 + -108 + 24x2 + -24x2 Combine like terms: 108 + -108 = 0 -108 + -24x2 + 4x4 = 0 + 24x2 + -24x2 -108 + -24x2 + 4x4 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -108 + -24x2 + 4x4 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -6x2 + x4) = 0 Factor a trinomial. 4((-3 + -1x2)(9 + -1x2)) = 0 Factor a difference between two squares. 4((-3 + -1x2)((3 + x)(3 + -1x))) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve: Simplifying -3 + -1x2 = 0 Solving -3 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x2 = 0 + 3 -1x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x2 = 3 Divide each side by '-1'. x2 = -3 Simplifying x2 = -3 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3, 3}
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