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Simplifying (22 + -1x)(18 + x) = 300 Multiply (22 + -1x) * (18 + x) (22(18 + x) + -1x * (18 + x)) = 300 ((18 * 22 + x * 22) + -1x * (18 + x)) = 300 ((396 + 22x) + -1x * (18 + x)) = 300 (396 + 22x + (18 * -1x + x * -1x)) = 300 (396 + 22x + (-18x + -1x2)) = 300 Combine like terms: 22x + -18x = 4x (396 + 4x + -1x2) = 300 Solving 396 + 4x + -1x2 = 300 Solving for variable 'x'. Reorder the terms: 396 + -300 + 4x + -1x2 = 300 + -300 Combine like terms: 396 + -300 = 96 96 + 4x + -1x2 = 300 + -300 Combine like terms: 300 + -300 = 0 96 + 4x + -1x2 = 0 Factor a trinomial. (12 + -1x)(8 + x) = 0Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {12, -8}
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