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Simplifying (x + 30)(x + 17) = 6120 Reorder the terms: (30 + x)(x + 17) = 6120 Reorder the terms: (30 + x)(17 + x) = 6120 Multiply (30 + x) * (17 + x) (30(17 + x) + x(17 + x)) = 6120 ((17 * 30 + x * 30) + x(17 + x)) = 6120 ((510 + 30x) + x(17 + x)) = 6120 (510 + 30x + (17 * x + x * x)) = 6120 (510 + 30x + (17x + x2)) = 6120 Combine like terms: 30x + 17x = 47x (510 + 47x + x2) = 6120 Solving 510 + 47x + x2 = 6120 Solving for variable 'x'. Reorder the terms: 510 + -6120 + 47x + x2 = 6120 + -6120 Combine like terms: 510 + -6120 = -5610 -5610 + 47x + x2 = 6120 + -6120 Combine like terms: 6120 + -6120 = 0 -5610 + 47x + x2 = 0 Factor a trinomial. (-102 + -1x)(55 + -1x) = 0Subproblem 1
Set the factor '(-102 + -1x)' equal to zero and attempt to solve: Simplifying -102 + -1x = 0 Solving -102 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '102' to each side of the equation. -102 + 102 + -1x = 0 + 102 Combine like terms: -102 + 102 = 0 0 + -1x = 0 + 102 -1x = 0 + 102 Combine like terms: 0 + 102 = 102 -1x = 102 Divide each side by '-1'. x = -102 Simplifying x = -102Subproblem 2
Set the factor '(55 + -1x)' equal to zero and attempt to solve: Simplifying 55 + -1x = 0 Solving 55 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + -1x = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -1x = 0 + -55 -1x = 0 + -55 Combine like terms: 0 + -55 = -55 -1x = -55 Divide each side by '-1'. x = 55 Simplifying x = 55Solution
x = {-102, 55}
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