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Simplifying (x + 1)(x + 2) = 110 Reorder the terms: (1 + x)(x + 2) = 110 Reorder the terms: (1 + x)(2 + x) = 110 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) = 110 ((2 * 1 + x * 1) + x(2 + x)) = 110 ((2 + 1x) + x(2 + x)) = 110 (2 + 1x + (2 * x + x * x)) = 110 (2 + 1x + (2x + x2)) = 110 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) = 110 Solving 2 + 3x + x2 = 110 Solving for variable 'x'. Reorder the terms: 2 + -110 + 3x + x2 = 110 + -110 Combine like terms: 2 + -110 = -108 -108 + 3x + x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -108 + 3x + x2 = 0 Factor a trinomial. (-12 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-12, 9}
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