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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 = -9x (14 + -9x + x2) + (x + 1)(x + -2) = 0 Reorder the terms: 14 + -9x + x2 + (1 + x)(x + -2) = 0 Reorder the terms: 14 + -9x + x2 + (1 + x)(-2 + x) = 0 Multiply (1 + x) * (-2 + x) 14 + -9x + x2 + (1(-2 + x) + x(-2 + x)) = 0 14 + -9x + x2 + ((-2 * 1 + x * 1) + x(-2 + x)) = 0 14 + -9x + x2 + ((-2 + 1x) + x(-2 + x)) = 0 14 + -9x + x2 + (-2 + 1x + (-2 * x + x * x)) = 0 14 + -9x + x2 + (-2 + 1x + (-2x + x2)) = 0 Combine like terms: 1x + -2x = -1x 14 + -9x + x2 + (-2 + -1x + x2) = 0 Reorder the terms: 14 + -2 + -9x + -1x + x2 + x2 = 0 Combine like terms: 14 + -2 = 12 12 + -9x + -1x + x2 + x2 = 0 Combine like terms: -9x + -1x = -10x 12 + -10x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 12 + -10x + 2x2 = 0 Solving 12 + -10x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -5x + x2) = 0 Factor a trinomial. 2((2 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = 2Subproblem 2
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 = {2, 3}
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