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Simplifying (40 + x) * x = 6000 Reorder the terms for easier multiplication: x(40 + x) = 6000 (40 * x + x * x) = 6000 (40x + x2) = 6000 Solving 40x + x2 = 6000 Solving for variable 'x'. Reorder the terms: -6000 + 40x + x2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -6000 + 40x + x2 = 0 Factor a trinomial. (-100 + -1x)(60 + -1x) = 0Subproblem 1
Set the factor '(-100 + -1x)' equal to zero and attempt to solve: Simplifying -100 + -1x = 0 Solving -100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + -1x = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -1x = 0 + 100 -1x = 0 + 100 Combine like terms: 0 + 100 = 100 -1x = 100 Divide each side by '-1'. x = -100 Simplifying x = -100Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Solution
x = {-100, 60}
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