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Simplifying (10x + 5)(x + -9) = 0 Reorder the terms: (5 + 10x)(x + -9) = 0 Reorder the terms: (5 + 10x)(-9 + x) = 0 Multiply (5 + 10x) * (-9 + x) (5(-9 + x) + 10x * (-9 + x)) = 0 ((-9 * 5 + x * 5) + 10x * (-9 + x)) = 0 ((-45 + 5x) + 10x * (-9 + x)) = 0 (-45 + 5x + (-9 * 10x + x * 10x)) = 0 (-45 + 5x + (-90x + 10x2)) = 0 Combine like terms: 5x + -90x = -85x (-45 + -85x + 10x2) = 0 Solving -45 + -85x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -17x + 2x2) = 0 Factor a trinomial. 5((-1 + -2x)(9 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-0.5, 9}
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