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Simplifying 48m2 + -119m + -246 = 0 Reorder the terms: -246 + -119m + 48m2 = 0 Solving -246 + -119m + 48m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -5.125 + -2.479166667m + m2 = 0 Move the constant term to the right: Add '5.125' to each side of the equation. -5.125 + -2.479166667m + 5.125 + m2 = 0 + 5.125 Reorder the terms: -5.125 + 5.125 + -2.479166667m + m2 = 0 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + -2.479166667m + m2 = 0 + 5.125 -2.479166667m + m2 = 0 + 5.125 Combine like terms: 0 + 5.125 = 5.125 -2.479166667m + m2 = 5.125 The m term is -2.479166667m. Take half its coefficient (-1.239583334). Square it (1.536566842) and add it to both sides. Add '1.536566842' to each side of the equation. -2.479166667m + 1.536566842 + m2 = 5.125 + 1.536566842 Reorder the terms: 1.536566842 + -2.479166667m + m2 = 5.125 + 1.536566842 Combine like terms: 5.125 + 1.536566842 = 6.661566842 1.536566842 + -2.479166667m + m2 = 6.661566842 Factor a perfect square on the left side: (m + -1.239583334)(m + -1.239583334) = 6.661566842 Calculate the square root of the right side: 2.581001132 Break this problem into two subproblems by setting (m + -1.239583334) equal to 2.581001132 and -2.581001132.Subproblem 1
m + -1.239583334 = 2.581001132 Simplifying m + -1.239583334 = 2.581001132 Reorder the terms: -1.239583334 + m = 2.581001132 Solving -1.239583334 + m = 2.581001132 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.239583334' to each side of the equation. -1.239583334 + 1.239583334 + m = 2.581001132 + 1.239583334 Combine like terms: -1.239583334 + 1.239583334 = 0.000000000 0.000000000 + m = 2.581001132 + 1.239583334 m = 2.581001132 + 1.239583334 Combine like terms: 2.581001132 + 1.239583334 = 3.820584466 m = 3.820584466 Simplifying m = 3.820584466Subproblem 2
m + -1.239583334 = -2.581001132 Simplifying m + -1.239583334 = -2.581001132 Reorder the terms: -1.239583334 + m = -2.581001132 Solving -1.239583334 + m = -2.581001132 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.239583334' to each side of the equation. -1.239583334 + 1.239583334 + m = -2.581001132 + 1.239583334 Combine like terms: -1.239583334 + 1.239583334 = 0.000000000 0.000000000 + m = -2.581001132 + 1.239583334 m = -2.581001132 + 1.239583334 Combine like terms: -2.581001132 + 1.239583334 = -1.341417798 m = -1.341417798 Simplifying m = -1.341417798Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.820584466, -1.341417798}
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