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Simplifying (15 + x)(8 + x) = 198 Multiply (15 + x) * (8 + x) (15(8 + x) + x(8 + x)) = 198 ((8 * 15 + x * 15) + x(8 + x)) = 198 ((120 + 15x) + x(8 + x)) = 198 (120 + 15x + (8 * x + x * x)) = 198 (120 + 15x + (8x + x2)) = 198 Combine like terms: 15x + 8x = 23x (120 + 23x + x2) = 198 Solving 120 + 23x + x2 = 198 Solving for variable 'x'. Reorder the terms: 120 + -198 + 23x + x2 = 198 + -198 Combine like terms: 120 + -198 = -78 -78 + 23x + x2 = 198 + -198 Combine like terms: 198 + -198 = 0 -78 + 23x + x2 = 0 Factor a trinomial. (-26 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve: Simplifying -26 + -1x = 0 Solving -26 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + -1x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -1x = 0 + 26 -1x = 0 + 26 Combine like terms: 0 + 26 = 26 -1x = 26 Divide each side by '-1'. x = -26 Simplifying x = -26Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-26, 3}
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