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Simplifying (x2 + x)(x2 + -1x) = 12 Reorder the terms: (x + x2)(x2 + -1x) = 12 Reorder the terms: (x + x2)(-1x + x2) = 12 Multiply (x + x2) * (-1x + x2) (x(-1x + x2) + x2(-1x + x2)) = 12 ((-1x * x + x2 * x) + x2(-1x + x2)) = 12 ((-1x2 + x3) + x2(-1x + x2)) = 12 (-1x2 + x3 + (-1x * x2 + x2 * x2)) = 12 (-1x2 + x3 + (-1x3 + x4)) = 12 Combine like terms: x3 + -1x3 = 0 (-1x2 + 0 + x4) = 12 (-1x2 + x4) = 12 Solving -1x2 + x4 = 12 Solving for variable 'x'. Reorder the terms: -12 + -1x2 + x4 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -1x2 + x4 = 0 Factor a trinomial. (-3 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. (-3 + -1x2)((2 + x)(2 + -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 '(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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