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Simplifying x4 + -1x2 = 4x2 + 36 Reorder the terms: -1x2 + x4 = 4x2 + 36 Reorder the terms: -1x2 + x4 = 36 + 4x2 Solving -1x2 + x4 = 36 + 4x2 Solving for variable 'x'. Reorder the terms: -36 + -1x2 + -4x2 + x4 = 36 + 4x2 + -36 + -4x2 Combine like terms: -1x2 + -4x2 = -5x2 -36 + -5x2 + x4 = 36 + 4x2 + -36 + -4x2 Reorder the terms: -36 + -5x2 + x4 = 36 + -36 + 4x2 + -4x2 Combine like terms: 36 + -36 = 0 -36 + -5x2 + x4 = 0 + 4x2 + -4x2 -36 + -5x2 + x4 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -36 + -5x2 + x4 = 0 Factor a trinomial. (-4 + -1x2)(9 + -1x2) = 0 Factor a difference between two squares. (-4 + -1x2)((3 + x)(3 + -1x)) = 0Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve: Simplifying -4 + -1x2 = 0 Solving -4 + -1x2 = 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 + -1x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x2 = 0 + 4 -1x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x2 = 4 Divide each side by '-1'. x2 = -4 Simplifying x2 = -4 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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