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Simplifying x(x + -15) + x + (x + -2) + 32 = 120 Reorder the terms: x(-15 + x) + x + (x + -2) + 32 = 120 (-15 * x + x * x) + x + (x + -2) + 32 = 120 (-15x + x2) + x + (x + -2) + 32 = 120 Reorder the terms: -15x + x2 + x + (-2 + x) + 32 = 120 Remove parenthesis around (-2 + x) -15x + x2 + x + -2 + x + 32 = 120 Reorder the terms: -2 + 32 + -15x + x + x + x2 = 120 Combine like terms: -2 + 32 = 30 30 + -15x + x + x + x2 = 120 Combine like terms: -15x + x = -14x 30 + -14x + x + x2 = 120 Combine like terms: -14x + x = -13x 30 + -13x + x2 = 120 Solving 30 + -13x + x2 = 120 Solving for variable 'x'. Reorder the terms: 30 + -120 + -13x + x2 = 120 + -120 Combine like terms: 30 + -120 = -90 -90 + -13x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -90 + -13x + x2 = 0 Factor a trinomial. (-5 + -1x)(18 + -1x) = 0Subproblem 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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