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Simplifying (12 + x)(22 + x) = 504 Multiply (12 + x) * (22 + x) (12(22 + x) + x(22 + x)) = 504 ((22 * 12 + x * 12) + x(22 + x)) = 504 ((264 + 12x) + x(22 + x)) = 504 (264 + 12x + (22 * x + x * x)) = 504 (264 + 12x + (22x + x2)) = 504 Combine like terms: 12x + 22x = 34x (264 + 34x + x2) = 504 Solving 264 + 34x + x2 = 504 Solving for variable 'x'. Reorder the terms: 264 + -504 + 34x + x2 = 504 + -504 Combine like terms: 264 + -504 = -240 -240 + 34x + x2 = 504 + -504 Combine like terms: 504 + -504 = 0 -240 + 34x + x2 = 0 Factor a trinomial. (-40 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve: Simplifying -40 + -1x = 0 Solving -40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + -1x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1x = 0 + 40 -1x = 0 + 40 Combine like terms: 0 + 40 = 40 -1x = 40 Divide each side by '-1'. x = -40 Simplifying x = -40Subproblem 2
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 = 6Solution
x = {-40, 6}
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