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Simplifying 6m2 + 39m + -16 = 0 Reorder the terms: -16 + 39m + 6m2 = 0 Solving -16 + 39m + 6m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.666666667 + 6.5m + m2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 6.5m + 2.666666667 + m2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 6.5m + m2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 6.5m + m2 = 0 + 2.666666667 6.5m + m2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 6.5m + m2 = 2.666666667 The m term is 6.5m. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5m + 10.5625 + m2 = 2.666666667 + 10.5625 Reorder the terms: 10.5625 + 6.5m + m2 = 2.666666667 + 10.5625 Combine like terms: 2.666666667 + 10.5625 = 13.229166667 10.5625 + 6.5m + m2 = 13.229166667 Factor a perfect square on the left side: (m + 3.25)(m + 3.25) = 13.229166667 Calculate the square root of the right side: 3.637192141 Break this problem into two subproblems by setting (m + 3.25) equal to 3.637192141 and -3.637192141.Subproblem 1
m + 3.25 = 3.637192141 Simplifying m + 3.25 = 3.637192141 Reorder the terms: 3.25 + m = 3.637192141 Solving 3.25 + m = 3.637192141 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + m = 3.637192141 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = 3.637192141 + -3.25 m = 3.637192141 + -3.25 Combine like terms: 3.637192141 + -3.25 = 0.387192141 m = 0.387192141 Simplifying m = 0.387192141Subproblem 2
m + 3.25 = -3.637192141 Simplifying m + 3.25 = -3.637192141 Reorder the terms: 3.25 + m = -3.637192141 Solving 3.25 + m = -3.637192141 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + m = -3.637192141 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = -3.637192141 + -3.25 m = -3.637192141 + -3.25 Combine like terms: -3.637192141 + -3.25 = -6.887192141 m = -6.887192141 Simplifying m = -6.887192141Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.387192141, -6.887192141}
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