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Simplifying (x + 6)(2x + 6) = 680 Reorder the terms: (6 + x)(2x + 6) = 680 Reorder the terms: (6 + x)(6 + 2x) = 680 Multiply (6 + x) * (6 + 2x) (6(6 + 2x) + x(6 + 2x)) = 680 ((6 * 6 + 2x * 6) + x(6 + 2x)) = 680 ((36 + 12x) + x(6 + 2x)) = 680 (36 + 12x + (6 * x + 2x * x)) = 680 (36 + 12x + (6x + 2x2)) = 680 Combine like terms: 12x + 6x = 18x (36 + 18x + 2x2) = 680 Solving 36 + 18x + 2x2 = 680 Solving for variable 'x'. Reorder the terms: 36 + -680 + 18x + 2x2 = 680 + -680 Combine like terms: 36 + -680 = -644 -644 + 18x + 2x2 = 680 + -680 Combine like terms: 680 + -680 = 0 -644 + 18x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-322 + 9x + x2) = 0 Factor a trinomial. 2((-23 + -1x)(14 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve: Simplifying -23 + -1x = 0 Solving -23 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1x = 0 + 23 -1x = 0 + 23 Combine like terms: 0 + 23 = 23 -1x = 23 Divide each side by '-1'. x = -23 Simplifying x = -23Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-23, 14}
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