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Simplifying (680 + -20x)(70 + 5x) = 0 Multiply (680 + -20x) * (70 + 5x) (680(70 + 5x) + -20x * (70 + 5x)) = 0 ((70 * 680 + 5x * 680) + -20x * (70 + 5x)) = 0 ((47600 + 3400x) + -20x * (70 + 5x)) = 0 (47600 + 3400x + (70 * -20x + 5x * -20x)) = 0 (47600 + 3400x + (-1400x + -100x2)) = 0 Combine like terms: 3400x + -1400x = 2000x (47600 + 2000x + -100x2) = 0 Solving 47600 + 2000x + -100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '100'. 100(476 + 20x + -1x2) = 0 Factor a trinomial. 100((34 + -1x)(14 + x)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(34 + -1x)' equal to zero and attempt to solve: Simplifying 34 + -1x = 0 Solving 34 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + -1x = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -1x = 0 + -34 -1x = 0 + -34 Combine like terms: 0 + -34 = -34 -1x = -34 Divide each side by '-1'. x = 34 Simplifying x = 34Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 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 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Solution
x = {34, -14}
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