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Simplifying 3680 = -10x2 + 285x + 2700 Reorder the terms: 3680 = 2700 + 285x + -10x2 Solving 3680 = 2700 + 285x + -10x2 Solving for variable 'x'. Combine like terms: 3680 + -2700 = 980 980 + -285x + 10x2 = 2700 + 285x + -10x2 + -2700 + -285x + 10x2 Reorder the terms: 980 + -285x + 10x2 = 2700 + -2700 + 285x + -285x + -10x2 + 10x2 Combine like terms: 2700 + -2700 = 0 980 + -285x + 10x2 = 0 + 285x + -285x + -10x2 + 10x2 980 + -285x + 10x2 = 285x + -285x + -10x2 + 10x2 Combine like terms: 285x + -285x = 0 980 + -285x + 10x2 = 0 + -10x2 + 10x2 980 + -285x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 980 + -285x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(196 + -57x + 2x2) = 0 Factor a trinomial. 5((4 + -1x)(49 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(49 + -2x)' equal to zero and attempt to solve: Simplifying 49 + -2x = 0 Solving 49 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + -2x = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -2x = 0 + -49 -2x = 0 + -49 Combine like terms: 0 + -49 = -49 -2x = -49 Divide each side by '-2'. x = 24.5 Simplifying x = 24.5Solution
x = {4, 24.5}
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