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Simplifying 6000 = (x + 40) * x Reorder the terms: 6000 = (40 + x) * x Reorder the terms for easier multiplication: 6000 = x(40 + x) 6000 = (40 * x + x * x) 6000 = (40x + x2) Solving 6000 = 40x + x2 Solving for variable 'x'. Reorder the terms: 6000 + -40x + -1x2 = 40x + -40x + x2 + -1x2 Combine like terms: 40x + -40x = 0 6000 + -40x + -1x2 = 0 + x2 + -1x2 6000 + -40x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6000 + -40x + -1x2 = 0 Factor a trinomial. (60 + -1x)(100 + x) = 0Subproblem 1
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 = 60Subproblem 2
Set the factor '(100 + x)' equal to zero and attempt to solve: Simplifying 100 + x = 0 Solving 100 + x = 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 + x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + x = 0 + -100 x = 0 + -100 Combine like terms: 0 + -100 = -100 x = -100 Simplifying x = -100Solution
x = {60, -100}
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