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Simplifying 29x(x + 3) = 9860 Reorder the terms: 29x(3 + x) = 9860 (3 * 29x + x * 29x) = 9860 (87x + 29x2) = 9860 Solving 87x + 29x2 = 9860 Solving for variable 'x'. Reorder the terms: -9860 + 87x + 29x2 = 9860 + -9860 Combine like terms: 9860 + -9860 = 0 -9860 + 87x + 29x2 = 0 Factor out the Greatest Common Factor (GCF), '29'. 29(-340 + 3x + x2) = 0 Factor a trinomial. 29((-20 + -1x)(17 + -1x)) = 0 Ignore the factor 29.Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 2
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 = 17Solution
x = {-20, 17}
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