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Simplifying 112000 = -40x2 + 4400x Reorder the terms: 112000 = 4400x + -40x2 Solving 112000 = 4400x + -40x2 Solving for variable 'x'. Reorder the terms: 112000 + -4400x + 40x2 = 4400x + -4400x + -40x2 + 40x2 Combine like terms: 4400x + -4400x = 0 112000 + -4400x + 40x2 = 0 + -40x2 + 40x2 112000 + -4400x + 40x2 = -40x2 + 40x2 Combine like terms: -40x2 + 40x2 = 0 112000 + -4400x + 40x2 = 0 Factor out the Greatest Common Factor (GCF), '40'. 40(2800 + -110x + x2) = 0 Factor a trinomial. 40((40 + -1x)(70 + -1x)) = 0 Ignore the factor 40.Subproblem 1
Set the factor '(40 + -1x)' equal to zero and attempt to solve: Simplifying 40 + -1x = 0 Solving 40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1x = 0 + -40 -1x = 0 + -40 Combine like terms: 0 + -40 = -40 -1x = -40 Divide each side by '-1'. x = 40 Simplifying x = 40Subproblem 2
Set the factor '(70 + -1x)' equal to zero and attempt to solve: Simplifying 70 + -1x = 0 Solving 70 + -1x = 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 + -1x = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1x = 0 + -70 -1x = 0 + -70 Combine like terms: 0 + -70 = -70 -1x = -70 Divide each side by '-1'. x = 70 Simplifying x = 70Solution
x = {40, 70}
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