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Simplifying (5 + x)(8 + x) = 154 Multiply (5 + x) * (8 + x) (5(8 + x) + x(8 + x)) = 154 ((8 * 5 + x * 5) + x(8 + x)) = 154 ((40 + 5x) + x(8 + x)) = 154 (40 + 5x + (8 * x + x * x)) = 154 (40 + 5x + (8x + x2)) = 154 Combine like terms: 5x + 8x = 13x (40 + 13x + x2) = 154 Solving 40 + 13x + x2 = 154 Solving for variable 'x'. Reorder the terms: 40 + -154 + 13x + x2 = 154 + -154 Combine like terms: 40 + -154 = -114 -114 + 13x + x2 = 154 + -154 Combine like terms: 154 + -154 = 0 -114 + 13x + x2 = 0 Factor a trinomial. (-19 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve: Simplifying -19 + -1x = 0 Solving -19 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -1x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1x = 0 + 19 -1x = 0 + 19 Combine like terms: 0 + 19 = 19 -1x = 19 Divide each side by '-1'. x = -19 Simplifying x = -19Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-19, 6}
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