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Simplifying 23x = 120 + x2 Solving 23x = 120 + x2 Solving for variable 'x'. Reorder the terms: -120 + 23x + -1x2 = 120 + x2 + -120 + -1x2 Reorder the terms: -120 + 23x + -1x2 = 120 + -120 + x2 + -1x2 Combine like terms: 120 + -120 = 0 -120 + 23x + -1x2 = 0 + x2 + -1x2 -120 + 23x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -120 + 23x + -1x2 = 0 Factor a trinomial. (-15 + x)(8 + -1x) = 0Subproblem 1
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 = 15Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {15, 8}
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