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Simplifying 105 = (X + 10)(2 + X) Reorder the terms: 105 = (10 + X)(2 + X) Multiply (10 + X) * (2 + X) 105 = (10(2 + X) + X(2 + X)) 105 = ((2 * 10 + X * 10) + X(2 + X)) 105 = ((20 + 10X) + X(2 + X)) 105 = (20 + 10X + (2 * X + X * X)) 105 = (20 + 10X + (2X + X2)) Combine like terms: 10X + 2X = 12X 105 = (20 + 12X + X2) Solving 105 = 20 + 12X + X2 Solving for variable 'X'. Combine like terms: 105 + -20 = 85 85 + -12X + -1X2 = 20 + 12X + X2 + -20 + -12X + -1X2 Reorder the terms: 85 + -12X + -1X2 = 20 + -20 + 12X + -12X + X2 + -1X2 Combine like terms: 20 + -20 = 0 85 + -12X + -1X2 = 0 + 12X + -12X + X2 + -1X2 85 + -12X + -1X2 = 12X + -12X + X2 + -1X2 Combine like terms: 12X + -12X = 0 85 + -12X + -1X2 = 0 + X2 + -1X2 85 + -12X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 85 + -12X + -1X2 = 0 Factor a trinomial. (5 + -1X)(17 + X) = 0Subproblem 1
Set the factor '(5 + -1X)' equal to zero and attempt to solve: Simplifying 5 + -1X = 0 Solving 5 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1X = 0 + -5 -1X = 0 + -5 Combine like terms: 0 + -5 = -5 -1X = -5 Divide each side by '-1'. X = 5 Simplifying X = 5Subproblem 2
Set the factor '(17 + X)' equal to zero and attempt to solve: Simplifying 17 + X = 0 Solving 17 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + X = 0 + -17 Combine like terms: 17 + -17 = 0 0 + X = 0 + -17 X = 0 + -17 Combine like terms: 0 + -17 = -17 X = -17 Simplifying X = -17Solution
X = {5, -17}
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