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Simplifying 180 + -1x = 45x + -2x2 Solving 180 + -1x = 45x + -2x2 Solving for variable 'x'. Combine like terms: -1x + -45x = -46x 180 + -46x + 2x2 = 45x + -2x2 + -45x + 2x2 Reorder the terms: 180 + -46x + 2x2 = 45x + -45x + -2x2 + 2x2 Combine like terms: 45x + -45x = 0 180 + -46x + 2x2 = 0 + -2x2 + 2x2 180 + -46x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 180 + -46x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -23x + x2) = 0 Factor a trinomial. 2((5 + -1x)(18 + -1x)) = 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 '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Solution
x = {5, 18}
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