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Simplifying (120 + x2) + -1(200 + 11x) = 100 Remove parenthesis around (120 + x2) 120 + x2 + -1(200 + 11x) = 100 120 + x2 + (200 * -1 + 11x * -1) = 100 120 + x2 + (-200 + -11x) = 100 Reorder the terms: 120 + -200 + -11x + x2 = 100 Combine like terms: 120 + -200 = -80 -80 + -11x + x2 = 100 Solving -80 + -11x + x2 = 100 Solving for variable 'x'. Reorder the terms: -80 + -100 + -11x + x2 = 100 + -100 Combine like terms: -80 + -100 = -180 -180 + -11x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -180 + -11x + x2 = 0 Factor a trinomial. (-9 + -1x)(20 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {-9, 20}
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