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Simplifying 2x(x + 5) + -3(x + x + 2x + -1) = 9 + -5x + -1x * x Reorder the terms: 2x(5 + x) + -3(x + x + 2x + -1) = 9 + -5x + -1x * x (5 * 2x + x * 2x) + -3(x + x + 2x + -1) = 9 + -5x + -1x * x (10x + 2x2) + -3(x + x + 2x + -1) = 9 + -5x + -1x * x Reorder the terms: 10x + 2x2 + -3(-1 + x + x + 2x) = 9 + -5x + -1x * x Combine like terms: x + x = 2x 10x + 2x2 + -3(-1 + 2x + 2x) = 9 + -5x + -1x * x Combine like terms: 2x + 2x = 4x 10x + 2x2 + -3(-1 + 4x) = 9 + -5x + -1x * x 10x + 2x2 + (-1 * -3 + 4x * -3) = 9 + -5x + -1x * x 10x + 2x2 + (3 + -12x) = 9 + -5x + -1x * x Reorder the terms: 3 + 10x + -12x + 2x2 = 9 + -5x + -1x * x Combine like terms: 10x + -12x = -2x 3 + -2x + 2x2 = 9 + -5x + -1x * x Multiply x * x 3 + -2x + 2x2 = 9 + -5x + -1x2 Solving 3 + -2x + 2x2 = 9 + -5x + -1x2 Solving for variable 'x'. Reorder the terms: 3 + -9 + -2x + 5x + 2x2 + x2 = 9 + -5x + -1x2 + -9 + 5x + x2 Combine like terms: 3 + -9 = -6 -6 + -2x + 5x + 2x2 + x2 = 9 + -5x + -1x2 + -9 + 5x + x2 Combine like terms: -2x + 5x = 3x -6 + 3x + 2x2 + x2 = 9 + -5x + -1x2 + -9 + 5x + x2 Combine like terms: 2x2 + x2 = 3x2 -6 + 3x + 3x2 = 9 + -5x + -1x2 + -9 + 5x + x2 Reorder the terms: -6 + 3x + 3x2 = 9 + -9 + -5x + 5x + -1x2 + x2 Combine like terms: 9 + -9 = 0 -6 + 3x + 3x2 = 0 + -5x + 5x + -1x2 + x2 -6 + 3x + 3x2 = -5x + 5x + -1x2 + x2 Combine like terms: -5x + 5x = 0 -6 + 3x + 3x2 = 0 + -1x2 + x2 -6 + 3x + 3x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -6 + 3x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + x + x2) = 0 Factor a trinomial. 3((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 3.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 '(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 = 1Solution
x = {-2, 1}
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