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Simplifying (x2 + -3)(x2 + -3) + (x2 + -3) + -2 = 0 Reorder the terms: (-3 + x2)(x2 + -3) + (x2 + -3) + -2 = 0 Reorder the terms: (-3 + x2)(-3 + x2) + (x2 + -3) + -2 = 0 Multiply (-3 + x2) * (-3 + x2) (-3(-3 + x2) + x2(-3 + x2)) + (x2 + -3) + -2 = 0 ((-3 * -3 + x2 * -3) + x2(-3 + x2)) + (x2 + -3) + -2 = 0 ((9 + -3x2) + x2(-3 + x2)) + (x2 + -3) + -2 = 0 (9 + -3x2 + (-3 * x2 + x2 * x2)) + (x2 + -3) + -2 = 0 (9 + -3x2 + (-3x2 + x4)) + (x2 + -3) + -2 = 0 Combine like terms: -3x2 + -3x2 = -6x2 (9 + -6x2 + x4) + (x2 + -3) + -2 = 0 Reorder the terms: 9 + -6x2 + x4 + (-3 + x2) + -2 = 0 Remove parenthesis around (-3 + x2) 9 + -6x2 + x4 + -3 + x2 + -2 = 0 Reorder the terms: 9 + -3 + -2 + -6x2 + x2 + x4 = 0 Combine like terms: 9 + -3 = 6 6 + -2 + -6x2 + x2 + x4 = 0 Combine like terms: 6 + -2 = 4 4 + -6x2 + x2 + x4 = 0 Combine like terms: -6x2 + x2 = -5x2 4 + -5x2 + x4 = 0 Solving 4 + -5x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(4 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(1 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 3
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 4
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 = {-1, 1, -2, 2}
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