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Simplifying 4125 = -10x2 + 235x + 3200 Reorder the terms: 4125 = 3200 + 235x + -10x2 Solving 4125 = 3200 + 235x + -10x2 Solving for variable 'x'. Combine like terms: 4125 + -3200 = 925 925 + -235x + 10x2 = 3200 + 235x + -10x2 + -3200 + -235x + 10x2 Reorder the terms: 925 + -235x + 10x2 = 3200 + -3200 + 235x + -235x + -10x2 + 10x2 Combine like terms: 3200 + -3200 = 0 925 + -235x + 10x2 = 0 + 235x + -235x + -10x2 + 10x2 925 + -235x + 10x2 = 235x + -235x + -10x2 + 10x2 Combine like terms: 235x + -235x = 0 925 + -235x + 10x2 = 0 + -10x2 + 10x2 925 + -235x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 925 + -235x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(185 + -47x + 2x2) = 0 Factor a trinomial. 5((5 + -1x)(37 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(37 + -2x)' equal to zero and attempt to solve: Simplifying 37 + -2x = 0 Solving 37 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + -2x = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -2x = 0 + -37 -2x = 0 + -37 Combine like terms: 0 + -37 = -37 -2x = -37 Divide each side by '-2'. x = 18.5 Simplifying x = 18.5Solution
x = {5, 18.5}
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