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Simplifying -10(x + -9)(x + -1) + -10(x + -2)(x + -1) = 0 Reorder the terms: -10(-9 + x)(x + -1) + -10(x + -2)(x + -1) = 0 Reorder the terms: -10(-9 + x)(-1 + x) + -10(x + -2)(x + -1) = 0 Multiply (-9 + x) * (-1 + x) -10(-9(-1 + x) + x(-1 + x)) + -10(x + -2)(x + -1) = 0 -10((-1 * -9 + x * -9) + x(-1 + x)) + -10(x + -2)(x + -1) = 0 -10((9 + -9x) + x(-1 + x)) + -10(x + -2)(x + -1) = 0 -10(9 + -9x + (-1 * x + x * x)) + -10(x + -2)(x + -1) = 0 -10(9 + -9x + (-1x + x2)) + -10(x + -2)(x + -1) = 0 Combine like terms: -9x + -1x = -10x -10(9 + -10x + x2) + -10(x + -2)(x + -1) = 0 (9 * -10 + -10x * -10 + x2 * -10) + -10(x + -2)(x + -1) = 0 (-90 + 100x + -10x2) + -10(x + -2)(x + -1) = 0 Reorder the terms: -90 + 100x + -10x2 + -10(-2 + x)(x + -1) = 0 Reorder the terms: -90 + 100x + -10x2 + -10(-2 + x)(-1 + x) = 0 Multiply (-2 + x) * (-1 + x) -90 + 100x + -10x2 + -10(-2(-1 + x) + x(-1 + x)) = 0 -90 + 100x + -10x2 + -10((-1 * -2 + x * -2) + x(-1 + x)) = 0 -90 + 100x + -10x2 + -10((2 + -2x) + x(-1 + x)) = 0 -90 + 100x + -10x2 + -10(2 + -2x + (-1 * x + x * x)) = 0 -90 + 100x + -10x2 + -10(2 + -2x + (-1x + x2)) = 0 Combine like terms: -2x + -1x = -3x -90 + 100x + -10x2 + -10(2 + -3x + x2) = 0 -90 + 100x + -10x2 + (2 * -10 + -3x * -10 + x2 * -10) = 0 -90 + 100x + -10x2 + (-20 + 30x + -10x2) = 0 Reorder the terms: -90 + -20 + 100x + 30x + -10x2 + -10x2 = 0 Combine like terms: -90 + -20 = -110 -110 + 100x + 30x + -10x2 + -10x2 = 0 Combine like terms: 100x + 30x = 130x -110 + 130x + -10x2 + -10x2 = 0 Combine like terms: -10x2 + -10x2 = -20x2 -110 + 130x + -20x2 = 0 Solving -110 + 130x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-11 + 13x + -2x2) = 0 Factor a trinomial. 10((-11 + 2x)(1 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-11 + 2x)' equal to zero and attempt to solve: Simplifying -11 + 2x = 0 Solving -11 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x = 0 + 11 2x = 0 + 11 Combine like terms: 0 + 11 = 11 2x = 11 Divide each side by '2'. x = 5.5 Simplifying x = 5.5Subproblem 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 = {5.5, 1}
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