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Simplifying 84 = x2 + 11x + 24 Reorder the terms: 84 = 24 + 11x + x2 Solving 84 = 24 + 11x + x2 Solving for variable 'x'. Combine like terms: 84 + -24 = 60 60 + -11x + -1x2 = 24 + 11x + x2 + -24 + -11x + -1x2 Reorder the terms: 60 + -11x + -1x2 = 24 + -24 + 11x + -11x + x2 + -1x2 Combine like terms: 24 + -24 = 0 60 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2 60 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 60 + -11x + -1x2 = 0 + x2 + -1x2 60 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 60 + -11x + -1x2 = 0 Factor a trinomial. (4 + -1x)(15 + x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Solution
x = {4, -15}
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