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Simplifying 150 + -10x + -1x2 = -50 + 20x + x2 Solving 150 + -10x + -1x2 = -50 + 20x + x2 Solving for variable 'x'. Reorder the terms: 150 + 50 + -10x + -20x + -1x2 + -1x2 = -50 + 20x + x2 + 50 + -20x + -1x2 Combine like terms: 150 + 50 = 200 200 + -10x + -20x + -1x2 + -1x2 = -50 + 20x + x2 + 50 + -20x + -1x2 Combine like terms: -10x + -20x = -30x 200 + -30x + -1x2 + -1x2 = -50 + 20x + x2 + 50 + -20x + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 200 + -30x + -2x2 = -50 + 20x + x2 + 50 + -20x + -1x2 Reorder the terms: 200 + -30x + -2x2 = -50 + 50 + 20x + -20x + x2 + -1x2 Combine like terms: -50 + 50 = 0 200 + -30x + -2x2 = 0 + 20x + -20x + x2 + -1x2 200 + -30x + -2x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 200 + -30x + -2x2 = 0 + x2 + -1x2 200 + -30x + -2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 200 + -30x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(100 + -15x + -1x2) = 0 Factor a trinomial. 2((5 + -1x)(20 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 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 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20Solution
x = {5, -20}
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