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Simplifying 3825 = -10x2 + 275x + 2700 Reorder the terms: 3825 = 2700 + 275x + -10x2 Solving 3825 = 2700 + 275x + -10x2 Solving for variable 'x'. Combine like terms: 3825 + -2700 = 1125 1125 + -275x + 10x2 = 2700 + 275x + -10x2 + -2700 + -275x + 10x2 Reorder the terms: 1125 + -275x + 10x2 = 2700 + -2700 + 275x + -275x + -10x2 + 10x2 Combine like terms: 2700 + -2700 = 0 1125 + -275x + 10x2 = 0 + 275x + -275x + -10x2 + 10x2 1125 + -275x + 10x2 = 275x + -275x + -10x2 + 10x2 Combine like terms: 275x + -275x = 0 1125 + -275x + 10x2 = 0 + -10x2 + 10x2 1125 + -275x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 1125 + -275x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(225 + -55x + 2x2) = 0 Factor a trinomial. 5((5 + -1x)(45 + -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 '(45 + -2x)' equal to zero and attempt to solve: Simplifying 45 + -2x = 0 Solving 45 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + -2x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -2x = 0 + -45 -2x = 0 + -45 Combine like terms: 0 + -45 = -45 -2x = -45 Divide each side by '-2'. x = 22.5 Simplifying x = 22.5Solution
x = {5, 22.5}
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