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Simplifying (x + 7)(x + -2) + (x + 1)(x + -2) = 0 Reorder the terms: (7 + x)(x + -2) + (x + 1)(x + -2) = 0 Reorder the terms: (7 + x)(-2 + x) + (x + 1)(x + -2) = 0 Multiply (7 + x) * (-2 + x) (7(-2 + x) + x(-2 + x)) + (x + 1)(x + -2) = 0 ((-2 * 7 + x * 7) + x(-2 + x)) + (x + 1)(x + -2) = 0 ((-14 + 7x) + x(-2 + x)) + (x + 1)(x + -2) = 0 (-14 + 7x + (-2 * x + x * x)) + (x + 1)(x + -2) = 0 (-14 + 7x + (-2x + x2)) + (x + 1)(x + -2) = 0 Combine like terms: 7x + -2x = 5x (-14 + 5x + x2) + (x + 1)(x + -2) = 0 Reorder the terms: -14 + 5x + x2 + (1 + x)(x + -2) = 0 Reorder the terms: -14 + 5x + x2 + (1 + x)(-2 + x) = 0 Multiply (1 + x) * (-2 + x) -14 + 5x + x2 + (1(-2 + x) + x(-2 + x)) = 0 -14 + 5x + x2 + ((-2 * 1 + x * 1) + x(-2 + x)) = 0 -14 + 5x + x2 + ((-2 + 1x) + x(-2 + x)) = 0 -14 + 5x + x2 + (-2 + 1x + (-2 * x + x * x)) = 0 -14 + 5x + x2 + (-2 + 1x + (-2x + x2)) = 0 Combine like terms: 1x + -2x = -1x -14 + 5x + x2 + (-2 + -1x + x2) = 0 Reorder the terms: -14 + -2 + 5x + -1x + x2 + x2 = 0 Combine like terms: -14 + -2 = -16 -16 + 5x + -1x + x2 + x2 = 0 Combine like terms: 5x + -1x = 4x -16 + 4x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -16 + 4x + 2x2 = 0 Solving -16 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 2x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 2
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 = {-4, 2}
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