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Simplifying 12065 = x2 + 20x + 65 Reorder the terms: 12065 = 65 + 20x + x2 Solving 12065 = 65 + 20x + x2 Solving for variable 'x'. Combine like terms: 12065 + -65 = 12000 12000 + -20x + -1x2 = 65 + 20x + x2 + -65 + -20x + -1x2 Reorder the terms: 12000 + -20x + -1x2 = 65 + -65 + 20x + -20x + x2 + -1x2 Combine like terms: 65 + -65 = 0 12000 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 12000 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 12000 + -20x + -1x2 = 0 + x2 + -1x2 12000 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12000 + -20x + -1x2 = 0 Factor a trinomial. (100 + -1x)(120 + x) = 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 '(120 + x)' equal to zero and attempt to solve: Simplifying 120 + x = 0 Solving 120 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-120' to each side of the equation. 120 + -120 + x = 0 + -120 Combine like terms: 120 + -120 = 0 0 + x = 0 + -120 x = 0 + -120 Combine like terms: 0 + -120 = -120 x = -120 Simplifying x = -120Solution
x = {100, -120}
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