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Simplifying 5350 = -10x2 + 325x + 3100 Reorder the terms: 5350 = 3100 + 325x + -10x2 Solving 5350 = 3100 + 325x + -10x2 Solving for variable 'x'. Combine like terms: 5350 + -3100 = 2250 2250 + -325x + 10x2 = 3100 + 325x + -10x2 + -3100 + -325x + 10x2 Reorder the terms: 2250 + -325x + 10x2 = 3100 + -3100 + 325x + -325x + -10x2 + 10x2 Combine like terms: 3100 + -3100 = 0 2250 + -325x + 10x2 = 0 + 325x + -325x + -10x2 + 10x2 2250 + -325x + 10x2 = 325x + -325x + -10x2 + 10x2 Combine like terms: 325x + -325x = 0 2250 + -325x + 10x2 = 0 + -10x2 + 10x2 2250 + -325x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 2250 + -325x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(450 + -65x + 2x2) = 0 Factor a trinomial. 5((10 + -1x)(45 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 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 = {10, 22.5}
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