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Simplifying 3780 = -10x2 + 235x + 3000 Reorder the terms: 3780 = 3000 + 235x + -10x2 Solving 3780 = 3000 + 235x + -10x2 Solving for variable 'x'. Combine like terms: 3780 + -3000 = 780 780 + -235x + 10x2 = 3000 + 235x + -10x2 + -3000 + -235x + 10x2 Reorder the terms: 780 + -235x + 10x2 = 3000 + -3000 + 235x + -235x + -10x2 + 10x2 Combine like terms: 3000 + -3000 = 0 780 + -235x + 10x2 = 0 + 235x + -235x + -10x2 + 10x2 780 + -235x + 10x2 = 235x + -235x + -10x2 + 10x2 Combine like terms: 235x + -235x = 0 780 + -235x + 10x2 = 0 + -10x2 + 10x2 780 + -235x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 780 + -235x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(156 + -47x + 2x2) = 0 Factor a trinomial. 5((4 + -1x)(39 + -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 '(39 + -2x)' equal to zero and attempt to solve: Simplifying 39 + -2x = 0 Solving 39 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + -2x = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -2x = 0 + -39 -2x = 0 + -39 Combine like terms: 0 + -39 = -39 -2x = -39 Divide each side by '-2'. x = 19.5 Simplifying x = 19.5Solution
x = {4, 19.5}
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