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Simplifying 252 = (8 + x)(12 + x) Multiply (8 + x) * (12 + x) 252 = (8(12 + x) + x(12 + x)) 252 = ((12 * 8 + x * 8) + x(12 + x)) 252 = ((96 + 8x) + x(12 + x)) 252 = (96 + 8x + (12 * x + x * x)) 252 = (96 + 8x + (12x + x2)) Combine like terms: 8x + 12x = 20x 252 = (96 + 20x + x2) Solving 252 = 96 + 20x + x2 Solving for variable 'x'. Combine like terms: 252 + -96 = 156 156 + -20x + -1x2 = 96 + 20x + x2 + -96 + -20x + -1x2 Reorder the terms: 156 + -20x + -1x2 = 96 + -96 + 20x + -20x + x2 + -1x2 Combine like terms: 96 + -96 = 0 156 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 156 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 156 + -20x + -1x2 = 0 + x2 + -1x2 156 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 156 + -20x + -1x2 = 0 Factor a trinomial. (6 + -1x)(26 + x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(26 + x)' equal to zero and attempt to solve: Simplifying 26 + x = 0 Solving 26 + x = 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 + x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + x = 0 + -26 x = 0 + -26 Combine like terms: 0 + -26 = -26 x = -26 Simplifying x = -26Solution
x = {6, -26}
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