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Simplifying (7 + x) * 2x = 340 Reorder the terms for easier multiplication: 2x(7 + x) = 340 (7 * 2x + x * 2x) = 340 (14x + 2x2) = 340 Solving 14x + 2x2 = 340 Solving for variable 'x'. Reorder the terms: -340 + 14x + 2x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -340 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-170 + 7x + x2) = 0 Factor a trinomial. 2((-17 + -1x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve: Simplifying -17 + -1x = 0 Solving -17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x = 0 + 17 -1x = 0 + 17 Combine like terms: 0 + 17 = 17 -1x = 17 Divide each side by '-1'. x = -17 Simplifying x = -17Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-17, 10}
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