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Simplifying (100 + -1x)(300 + 20x) = 51000 Multiply (100 + -1x) * (300 + 20x) (100(300 + 20x) + -1x * (300 + 20x)) = 51000 ((300 * 100 + 20x * 100) + -1x * (300 + 20x)) = 51000 ((30000 + 2000x) + -1x * (300 + 20x)) = 51000 (30000 + 2000x + (300 * -1x + 20x * -1x)) = 51000 (30000 + 2000x + (-300x + -20x2)) = 51000 Combine like terms: 2000x + -300x = 1700x (30000 + 1700x + -20x2) = 51000 Solving 30000 + 1700x + -20x2 = 51000 Solving for variable 'x'. Reorder the terms: 30000 + -51000 + 1700x + -20x2 = 51000 + -51000 Combine like terms: 30000 + -51000 = -21000 -21000 + 1700x + -20x2 = 51000 + -51000 Combine like terms: 51000 + -51000 = 0 -21000 + 1700x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-1050 + 85x + -1x2) = 0 Factor a trinomial. 20((-70 + x)(15 + -1x)) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-70 + x)' equal to zero and attempt to solve: Simplifying -70 + x = 0 Solving -70 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + x = 0 + 70 Combine like terms: -70 + 70 = 0 0 + x = 0 + 70 x = 0 + 70 Combine like terms: 0 + 70 = 70 x = 70 Simplifying x = 70Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {70, 15}
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