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Simplifying x4 + -1x2 = 12x2 + 48 Reorder the terms: -1x2 + x4 = 12x2 + 48 Reorder the terms: -1x2 + x4 = 48 + 12x2 Solving -1x2 + x4 = 48 + 12x2 Solving for variable 'x'. Reorder the terms: -48 + -1x2 + -12x2 + x4 = 48 + 12x2 + -48 + -12x2 Combine like terms: -1x2 + -12x2 = -13x2 -48 + -13x2 + x4 = 48 + 12x2 + -48 + -12x2 Reorder the terms: -48 + -13x2 + x4 = 48 + -48 + 12x2 + -12x2 Combine like terms: 48 + -48 = 0 -48 + -13x2 + x4 = 0 + 12x2 + -12x2 -48 + -13x2 + x4 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -48 + -13x2 + x4 = 0 Factor a trinomial. (-3 + -1x2)(16 + -1x2) = 0 Factor a difference between two squares. (-3 + -1x2)((4 + x)(4 + -1x)) = 0Subproblem 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4, 4}
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