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Simplifying (x + 7)(x + 9) = 440 Reorder the terms: (7 + x)(x + 9) = 440 Reorder the terms: (7 + x)(9 + x) = 440 Multiply (7 + x) * (9 + x) (7(9 + x) + x(9 + x)) = 440 ((9 * 7 + x * 7) + x(9 + x)) = 440 ((63 + 7x) + x(9 + x)) = 440 (63 + 7x + (9 * x + x * x)) = 440 (63 + 7x + (9x + x2)) = 440 Combine like terms: 7x + 9x = 16x (63 + 16x + x2) = 440 Solving 63 + 16x + x2 = 440 Solving for variable 'x'. Reorder the terms: 63 + -440 + 16x + x2 = 440 + -440 Combine like terms: 63 + -440 = -377 -377 + 16x + x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -377 + 16x + x2 = 0 Factor a trinomial. (-29 + -1x)(13 + -1x) = 0Subproblem 1
Set the factor '(-29 + -1x)' equal to zero and attempt to solve: Simplifying -29 + -1x = 0 Solving -29 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + -1x = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -1x = 0 + 29 -1x = 0 + 29 Combine like terms: 0 + 29 = 29 -1x = 29 Divide each side by '-1'. x = -29 Simplifying x = -29Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-29, 13}
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