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Simplifying 19600x2 + 39200x = 2009 Reorder the terms: 39200x + 19600x2 = 2009 Solving 39200x + 19600x2 = 2009 Solving for variable 'x'. Reorder the terms: -2009 + 39200x + 19600x2 = 2009 + -2009 Combine like terms: 2009 + -2009 = 0 -2009 + 39200x + 19600x2 = 0 Factor out the Greatest Common Factor (GCF), '49'. 49(-41 + 800x + 400x2) = 0 Factor a trinomial. 49((-41 + -20x)(1 + -20x)) = 0 Ignore the factor 49.Subproblem 1
Set the factor '(-41 + -20x)' equal to zero and attempt to solve: Simplifying -41 + -20x = 0 Solving -41 + -20x = 0 Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + -20x = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -20x = 0 + 41 -20x = 0 + 41 Combine like terms: 0 + 41 = 41 -20x = 41 Divide each side by '-20'. x = -2.05 Simplifying x = -2.05Subproblem 2
Set the factor '(1 + -20x)' equal to zero and attempt to solve: Simplifying 1 + -20x = 0 Solving 1 + -20x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -20x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -20x = 0 + -1 -20x = 0 + -1 Combine like terms: 0 + -1 = -1 -20x = -1 Divide each side by '-20'. x = 0.05 Simplifying x = 0.05Solution
x = {-2.05, 0.05}
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