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Simplifying 9x(x + -2) = (2x + 7)(x + -2) Reorder the terms: 9x(-2 + x) = (2x + 7)(x + -2) (-2 * 9x + x * 9x) = (2x + 7)(x + -2) (-18x + 9x2) = (2x + 7)(x + -2) Reorder the terms: -18x + 9x2 = (7 + 2x)(x + -2) Reorder the terms: -18x + 9x2 = (7 + 2x)(-2 + x) Multiply (7 + 2x) * (-2 + x) -18x + 9x2 = (7(-2 + x) + 2x * (-2 + x)) -18x + 9x2 = ((-2 * 7 + x * 7) + 2x * (-2 + x)) -18x + 9x2 = ((-14 + 7x) + 2x * (-2 + x)) -18x + 9x2 = (-14 + 7x + (-2 * 2x + x * 2x)) -18x + 9x2 = (-14 + 7x + (-4x + 2x2)) Combine like terms: 7x + -4x = 3x -18x + 9x2 = (-14 + 3x + 2x2) Solving -18x + 9x2 = -14 + 3x + 2x2 Solving for variable 'x'. Reorder the terms: 14 + -18x + -3x + 9x2 + -2x2 = -14 + 3x + 2x2 + 14 + -3x + -2x2 Combine like terms: -18x + -3x = -21x 14 + -21x + 9x2 + -2x2 = -14 + 3x + 2x2 + 14 + -3x + -2x2 Combine like terms: 9x2 + -2x2 = 7x2 14 + -21x + 7x2 = -14 + 3x + 2x2 + 14 + -3x + -2x2 Reorder the terms: 14 + -21x + 7x2 = -14 + 14 + 3x + -3x + 2x2 + -2x2 Combine like terms: -14 + 14 = 0 14 + -21x + 7x2 = 0 + 3x + -3x + 2x2 + -2x2 14 + -21x + 7x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 14 + -21x + 7x2 = 0 + 2x2 + -2x2 14 + -21x + 7x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 14 + -21x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(2 + -3x + x2) = 0 Factor a trinomial. 7((1 + -1x)(2 + -1x)) = 0 Ignore the factor 7.Subproblem 1
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 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 = {1, 2}
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