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Simplifying (2m2 + 6m) + (m2 + 5m + 7) = 0 Reorder the terms: (6m + 2m2) + (m2 + 5m + 7) = 0 Remove parenthesis around (6m + 2m2) 6m + 2m2 + (m2 + 5m + 7) = 0 Reorder the terms: 6m + 2m2 + (7 + 5m + m2) = 0 Remove parenthesis around (7 + 5m + m2) 6m + 2m2 + 7 + 5m + m2 = 0 Reorder the terms: 7 + 6m + 5m + 2m2 + m2 = 0 Combine like terms: 6m + 5m = 11m 7 + 11m + 2m2 + m2 = 0 Combine like terms: 2m2 + m2 = 3m2 7 + 11m + 3m2 = 0 Solving 7 + 11m + 3m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 3.666666667m + m2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 3.666666667m + -2.333333333 + m2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 3.666666667m + m2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 3.666666667m + m2 = 0 + -2.333333333 3.666666667m + m2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 3.666666667m + m2 = -2.333333333 The m term is 3.666666667m. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667m + 3.361111114 + m2 = -2.333333333 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667m + m2 = -2.333333333 + 3.361111114 Combine like terms: -2.333333333 + 3.361111114 = 1.027777781 3.361111114 + 3.666666667m + m2 = 1.027777781 Factor a perfect square on the left side: (m + 1.833333334)(m + 1.833333334) = 1.027777781 Calculate the square root of the right side: 1.013793757 Break this problem into two subproblems by setting (m + 1.833333334) equal to 1.013793757 and -1.013793757.Subproblem 1
m + 1.833333334 = 1.013793757 Simplifying m + 1.833333334 = 1.013793757 Reorder the terms: 1.833333334 + m = 1.013793757 Solving 1.833333334 + m = 1.013793757 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + m = 1.013793757 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + m = 1.013793757 + -1.833333334 m = 1.013793757 + -1.833333334 Combine like terms: 1.013793757 + -1.833333334 = -0.819539577 m = -0.819539577 Simplifying m = -0.819539577Subproblem 2
m + 1.833333334 = -1.013793757 Simplifying m + 1.833333334 = -1.013793757 Reorder the terms: 1.833333334 + m = -1.013793757 Solving 1.833333334 + m = -1.013793757 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + m = -1.013793757 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + m = -1.013793757 + -1.833333334 m = -1.013793757 + -1.833333334 Combine like terms: -1.013793757 + -1.833333334 = -2.847127091 m = -2.847127091 Simplifying m = -2.847127091Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.819539577, -2.847127091}
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