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Simplifying 10m(5m + -9) = 39 Reorder the terms: 10m(-9 + 5m) = 39 (-9 * 10m + 5m * 10m) = 39 (-90m + 50m2) = 39 Solving -90m + 50m2 = 39 Solving for variable 'm'. Reorder the terms: -39 + -90m + 50m2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + -90m + 50m2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.78 + -1.8m + m2 = 0.0 Move the constant term to the right: Add '0.78' to each side of the equation. -0.78 + -1.8m + 0.78 + m2 = 0.0 + 0.78 Reorder the terms: -0.78 + 0.78 + -1.8m + m2 = 0.0 + 0.78 Combine like terms: -0.78 + 0.78 = 0.00 0.00 + -1.8m + m2 = 0.0 + 0.78 -1.8m + m2 = 0.0 + 0.78 Combine like terms: 0.0 + 0.78 = 0.78 -1.8m + m2 = 0.78 The m term is -1.8m. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8m + 0.81 + m2 = 0.78 + 0.81 Reorder the terms: 0.81 + -1.8m + m2 = 0.78 + 0.81 Combine like terms: 0.78 + 0.81 = 1.59 0.81 + -1.8m + m2 = 1.59 Factor a perfect square on the left side: (m + -0.9)(m + -0.9) = 1.59 Calculate the square root of the right side: 1.260952021 Break this problem into two subproblems by setting (m + -0.9) equal to 1.260952021 and -1.260952021.Subproblem 1
m + -0.9 = 1.260952021 Simplifying m + -0.9 = 1.260952021 Reorder the terms: -0.9 + m = 1.260952021 Solving -0.9 + m = 1.260952021 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + m = 1.260952021 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + m = 1.260952021 + 0.9 m = 1.260952021 + 0.9 Combine like terms: 1.260952021 + 0.9 = 2.160952021 m = 2.160952021 Simplifying m = 2.160952021Subproblem 2
m + -0.9 = -1.260952021 Simplifying m + -0.9 = -1.260952021 Reorder the terms: -0.9 + m = -1.260952021 Solving -0.9 + m = -1.260952021 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + m = -1.260952021 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + m = -1.260952021 + 0.9 m = -1.260952021 + 0.9 Combine like terms: -1.260952021 + 0.9 = -0.360952021 m = -0.360952021 Simplifying m = -0.360952021Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.160952021, -0.360952021}
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