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Simplifying (x * x + 2)(x * x + 2) + (x * x + 2) + -42 = 0 Multiply x * x (x2 + 2)(x * x + 2) + (x * x + 2) + -42 = 0 Reorder the terms: (2 + x2)(x * x + 2) + (x * x + 2) + -42 = 0 Multiply x * x (2 + x2)(x2 + 2) + (x * x + 2) + -42 = 0 Reorder the terms: (2 + x2)(2 + x2) + (x * x + 2) + -42 = 0 Multiply (2 + x2) * (2 + x2) (2(2 + x2) + x2(2 + x2)) + (x * x + 2) + -42 = 0 ((2 * 2 + x2 * 2) + x2(2 + x2)) + (x * x + 2) + -42 = 0 ((4 + 2x2) + x2(2 + x2)) + (x * x + 2) + -42 = 0 (4 + 2x2 + (2 * x2 + x2 * x2)) + (x * x + 2) + -42 = 0 (4 + 2x2 + (2x2 + x4)) + (x * x + 2) + -42 = 0 Combine like terms: 2x2 + 2x2 = 4x2 (4 + 4x2 + x4) + (x * x + 2) + -42 = 0 Multiply x * x 4 + 4x2 + x4 + (x2 + 2) + -42 = 0 Reorder the terms: 4 + 4x2 + x4 + (2 + x2) + -42 = 0 Remove parenthesis around (2 + x2) 4 + 4x2 + x4 + 2 + x2 + -42 = 0 Reorder the terms: 4 + 2 + -42 + 4x2 + x2 + x4 = 0 Combine like terms: 4 + 2 = 6 6 + -42 + 4x2 + x2 + x4 = 0 Combine like terms: 6 + -42 = -36 -36 + 4x2 + x2 + x4 = 0 Combine like terms: 4x2 + x2 = 5x2 -36 + 5x2 + x4 = 0 Solving -36 + 5x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (-9 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. (-9 + -1x2)((2 + x)(2 + -1x)) = 0Subproblem 1
Set the factor '(-9 + -1x2)' equal to zero and attempt to solve: Simplifying -9 + -1x2 = 0 Solving -9 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x2 = 0 + 9 -1x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1x2 = 9 Divide each side by '-1'. x2 = -9 Simplifying x2 = -9 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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