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Simplifying 6m2 + 7m + -110 = 0 Reorder the terms: -110 + 7m + 6m2 = 0 Solving -110 + 7m + 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'. -18.33333333 + 1.166666667m + m2 = 0 Move the constant term to the right: Add '18.33333333' to each side of the equation. -18.33333333 + 1.166666667m + 18.33333333 + m2 = 0 + 18.33333333 Reorder the terms: -18.33333333 + 18.33333333 + 1.166666667m + m2 = 0 + 18.33333333 Combine like terms: -18.33333333 + 18.33333333 = 0.00000000 0.00000000 + 1.166666667m + m2 = 0 + 18.33333333 1.166666667m + m2 = 0 + 18.33333333 Combine like terms: 0 + 18.33333333 = 18.33333333 1.166666667m + m2 = 18.33333333 The m term is 1.166666667m. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667m + 0.3402777780 + m2 = 18.33333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667m + m2 = 18.33333333 + 0.3402777780 Combine like terms: 18.33333333 + 0.3402777780 = 18.673611108 0.3402777780 + 1.166666667m + m2 = 18.673611108 Factor a perfect square on the left side: (m + 0.5833333335)(m + 0.5833333335) = 18.673611108 Calculate the square root of the right side: 4.321297387 Break this problem into two subproblems by setting (m + 0.5833333335) equal to 4.321297387 and -4.321297387.Subproblem 1
m + 0.5833333335 = 4.321297387 Simplifying m + 0.5833333335 = 4.321297387 Reorder the terms: 0.5833333335 + m = 4.321297387 Solving 0.5833333335 + m = 4.321297387 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + m = 4.321297387 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + m = 4.321297387 + -0.5833333335 m = 4.321297387 + -0.5833333335 Combine like terms: 4.321297387 + -0.5833333335 = 3.7379640535 m = 3.7379640535 Simplifying m = 3.7379640535Subproblem 2
m + 0.5833333335 = -4.321297387 Simplifying m + 0.5833333335 = -4.321297387 Reorder the terms: 0.5833333335 + m = -4.321297387 Solving 0.5833333335 + m = -4.321297387 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + m = -4.321297387 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + m = -4.321297387 + -0.5833333335 m = -4.321297387 + -0.5833333335 Combine like terms: -4.321297387 + -0.5833333335 = -4.9046307205 m = -4.9046307205 Simplifying m = -4.9046307205Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.7379640535, -4.9046307205}
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