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Simplifying 117 = (x + 2)(x + 6) Reorder the terms: 117 = (2 + x)(x + 6) Reorder the terms: 117 = (2 + x)(6 + x) Multiply (2 + x) * (6 + x) 117 = (2(6 + x) + x(6 + x)) 117 = ((6 * 2 + x * 2) + x(6 + x)) 117 = ((12 + 2x) + x(6 + x)) 117 = (12 + 2x + (6 * x + x * x)) 117 = (12 + 2x + (6x + x2)) Combine like terms: 2x + 6x = 8x 117 = (12 + 8x + x2) Solving 117 = 12 + 8x + x2 Solving for variable 'x'. Combine like terms: 117 + -12 = 105 105 + -8x + -1x2 = 12 + 8x + x2 + -12 + -8x + -1x2 Reorder the terms: 105 + -8x + -1x2 = 12 + -12 + 8x + -8x + x2 + -1x2 Combine like terms: 12 + -12 = 0 105 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 105 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 105 + -8x + -1x2 = 0 + x2 + -1x2 105 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 105 + -8x + -1x2 = 0 Factor a trinomial. (7 + -1x)(15 + x) = 0Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Solution
x = {7, -15}
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