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Simplifying 0 = x2 + -18x + 65 Reorder the terms: 0 = 65 + -18x + x2 Solving 0 = 65 + -18x + x2 Solving for variable 'x'. Combine like terms: 0 + -65 = -65 -65 + 18x + -1x2 = 65 + -18x + x2 + -65 + 18x + -1x2 Reorder the terms: -65 + 18x + -1x2 = 65 + -65 + -18x + 18x + x2 + -1x2 Combine like terms: 65 + -65 = 0 -65 + 18x + -1x2 = 0 + -18x + 18x + x2 + -1x2 -65 + 18x + -1x2 = -18x + 18x + x2 + -1x2 Combine like terms: -18x + 18x = 0 -65 + 18x + -1x2 = 0 + x2 + -1x2 -65 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -65 + 18x + -1x2 = 0 Factor a trinomial. (-13 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-13 + x)' equal to zero and attempt to solve: Simplifying -13 + x = 0 Solving -13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x = 0 + 13 x = 0 + 13 Combine like terms: 0 + 13 = 13 x = 13 Simplifying x = 13Subproblem 2
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 = 5Solution
x = {13, 5}
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