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Simplifying (x + -15)(x + 1) = 17 Reorder the terms: (-15 + x)(x + 1) = 17 Reorder the terms: (-15 + x)(1 + x) = 17 Multiply (-15 + x) * (1 + x) (-15(1 + x) + x(1 + x)) = 17 ((1 * -15 + x * -15) + x(1 + x)) = 17 ((-15 + -15x) + x(1 + x)) = 17 (-15 + -15x + (1 * x + x * x)) = 17 (-15 + -15x + (1x + x2)) = 17 Combine like terms: -15x + 1x = -14x (-15 + -14x + x2) = 17 Solving -15 + -14x + x2 = 17 Solving for variable 'x'. Reorder the terms: -15 + -17 + -14x + x2 = 17 + -17 Combine like terms: -15 + -17 = -32 -32 + -14x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -32 + -14x + x2 = 0 Factor a trinomial. (-2 + -1x)(16 + -1x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve: Simplifying 16 + -1x = 0 Solving 16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1x = 0 + -16 -1x = 0 + -16 Combine like terms: 0 + -16 = -16 -1x = -16 Divide each side by '-1'. x = 16 Simplifying x = 16Solution
x = {-2, 16}
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