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Simplifying 3250 + -1m = 2m(m + -500) + 1500 Reorder the terms: 3250 + -1m = 2m(-500 + m) + 1500 3250 + -1m = (-500 * 2m + m * 2m) + 1500 3250 + -1m = (-1000m + 2m2) + 1500 Reorder the terms: 3250 + -1m = 1500 + -1000m + 2m2 Solving 3250 + -1m = 1500 + -1000m + 2m2 Solving for variable 'm'. Reorder the terms: 3250 + -1500 + -1m + 1000m + -2m2 = 1500 + -1000m + 2m2 + -1500 + 1000m + -2m2 Combine like terms: 3250 + -1500 = 1750 1750 + -1m + 1000m + -2m2 = 1500 + -1000m + 2m2 + -1500 + 1000m + -2m2 Combine like terms: -1m + 1000m = 999m 1750 + 999m + -2m2 = 1500 + -1000m + 2m2 + -1500 + 1000m + -2m2 Reorder the terms: 1750 + 999m + -2m2 = 1500 + -1500 + -1000m + 1000m + 2m2 + -2m2 Combine like terms: 1500 + -1500 = 0 1750 + 999m + -2m2 = 0 + -1000m + 1000m + 2m2 + -2m2 1750 + 999m + -2m2 = -1000m + 1000m + 2m2 + -2m2 Combine like terms: -1000m + 1000m = 0 1750 + 999m + -2m2 = 0 + 2m2 + -2m2 1750 + 999m + -2m2 = 2m2 + -2m2 Combine like terms: 2m2 + -2m2 = 0 1750 + 999m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -875 + -499.5m + m2 = 0 Move the constant term to the right: Add '875' to each side of the equation. -875 + -499.5m + 875 + m2 = 0 + 875 Reorder the terms: -875 + 875 + -499.5m + m2 = 0 + 875 Combine like terms: -875 + 875 = 0 0 + -499.5m + m2 = 0 + 875 -499.5m + m2 = 0 + 875 Combine like terms: 0 + 875 = 875 -499.5m + m2 = 875 The m term is -499.5m. Take half its coefficient (-249.75). Square it (62375.0625) and add it to both sides. Add '62375.0625' to each side of the equation. -499.5m + 62375.0625 + m2 = 875 + 62375.0625 Reorder the terms: 62375.0625 + -499.5m + m2 = 875 + 62375.0625 Combine like terms: 875 + 62375.0625 = 63250.0625 62375.0625 + -499.5m + m2 = 63250.0625 Factor a perfect square on the left side: (m + -249.75)(m + -249.75) = 63250.0625 Calculate the square root of the right side: 251.495651056 Break this problem into two subproblems by setting (m + -249.75) equal to 251.495651056 and -251.495651056.Subproblem 1
m + -249.75 = 251.495651056 Simplifying m + -249.75 = 251.495651056 Reorder the terms: -249.75 + m = 251.495651056 Solving -249.75 + m = 251.495651056 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '249.75' to each side of the equation. -249.75 + 249.75 + m = 251.495651056 + 249.75 Combine like terms: -249.75 + 249.75 = 0.00 0.00 + m = 251.495651056 + 249.75 m = 251.495651056 + 249.75 Combine like terms: 251.495651056 + 249.75 = 501.245651056 m = 501.245651056 Simplifying m = 501.245651056Subproblem 2
m + -249.75 = -251.495651056 Simplifying m + -249.75 = -251.495651056 Reorder the terms: -249.75 + m = -251.495651056 Solving -249.75 + m = -251.495651056 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '249.75' to each side of the equation. -249.75 + 249.75 + m = -251.495651056 + 249.75 Combine like terms: -249.75 + 249.75 = 0.00 0.00 + m = -251.495651056 + 249.75 m = -251.495651056 + 249.75 Combine like terms: -251.495651056 + 249.75 = -1.745651056 m = -1.745651056 Simplifying m = -1.745651056Solution
The solution to the problem is based on the solutions from the subproblems. m = {501.245651056, -1.745651056}
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