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Simplifying 6m2 = 13m + 38 Reorder the terms: 6m2 = 38 + 13m Solving 6m2 = 38 + 13m Solving for variable 'm'. Reorder the terms: -38 + -13m + 6m2 = 38 + 13m + -38 + -13m Reorder the terms: -38 + -13m + 6m2 = 38 + -38 + 13m + -13m Combine like terms: 38 + -38 = 0 -38 + -13m + 6m2 = 0 + 13m + -13m -38 + -13m + 6m2 = 13m + -13m Combine like terms: 13m + -13m = 0 -38 + -13m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6.333333333 + -2.166666667m + m2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + -2.166666667m + 6.333333333 + m2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + -2.166666667m + m2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + -2.166666667m + m2 = 0 + 6.333333333 -2.166666667m + m2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 -2.166666667m + m2 = 6.333333333 The m term is -2.166666667m. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667m + 1.173611113 + m2 = 6.333333333 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667m + m2 = 6.333333333 + 1.173611113 Combine like terms: 6.333333333 + 1.173611113 = 7.506944446 1.173611113 + -2.166666667m + m2 = 7.506944446 Factor a perfect square on the left side: (m + -1.083333334)(m + -1.083333334) = 7.506944446 Calculate the square root of the right side: 2.739880371 Break this problem into two subproblems by setting (m + -1.083333334) equal to 2.739880371 and -2.739880371.Subproblem 1
m + -1.083333334 = 2.739880371 Simplifying m + -1.083333334 = 2.739880371 Reorder the terms: -1.083333334 + m = 2.739880371 Solving -1.083333334 + m = 2.739880371 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + m = 2.739880371 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + m = 2.739880371 + 1.083333334 m = 2.739880371 + 1.083333334 Combine like terms: 2.739880371 + 1.083333334 = 3.823213705 m = 3.823213705 Simplifying m = 3.823213705Subproblem 2
m + -1.083333334 = -2.739880371 Simplifying m + -1.083333334 = -2.739880371 Reorder the terms: -1.083333334 + m = -2.739880371 Solving -1.083333334 + m = -2.739880371 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + m = -2.739880371 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + m = -2.739880371 + 1.083333334 m = -2.739880371 + 1.083333334 Combine like terms: -2.739880371 + 1.083333334 = -1.656547037 m = -1.656547037 Simplifying m = -1.656547037Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.823213705, -1.656547037}
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