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Simplifying (3 + x)(8 + x) = 234 Multiply (3 + x) * (8 + x) (3(8 + x) + x(8 + x)) = 234 ((8 * 3 + x * 3) + x(8 + x)) = 234 ((24 + 3x) + x(8 + x)) = 234 (24 + 3x + (8 * x + x * x)) = 234 (24 + 3x + (8x + x2)) = 234 Combine like terms: 3x + 8x = 11x (24 + 11x + x2) = 234 Solving 24 + 11x + x2 = 234 Solving for variable 'x'. Reorder the terms: 24 + -234 + 11x + x2 = 234 + -234 Combine like terms: 24 + -234 = -210 -210 + 11x + x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -210 + 11x + x2 = 0 Factor a trinomial. (-21 + -1x)(10 + -1x) = 0Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve: Simplifying -21 + -1x = 0 Solving -21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1x = 0 + 21 -1x = 0 + 21 Combine like terms: 0 + 21 = 21 -1x = 21 Divide each side by '-1'. x = -21 Simplifying x = -21Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-21, 10}
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