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Simplifying 9m(m + 6) = 2(m + 1) Reorder the terms: 9m(6 + m) = 2(m + 1) (6 * 9m + m * 9m) = 2(m + 1) (54m + 9m2) = 2(m + 1) Reorder the terms: 54m + 9m2 = 2(1 + m) 54m + 9m2 = (1 * 2 + m * 2) 54m + 9m2 = (2 + 2m) Solving 54m + 9m2 = 2 + 2m Solving for variable 'm'. Reorder the terms: -2 + 54m + -2m + 9m2 = 2 + 2m + -2 + -2m Combine like terms: 54m + -2m = 52m -2 + 52m + 9m2 = 2 + 2m + -2 + -2m Reorder the terms: -2 + 52m + 9m2 = 2 + -2 + 2m + -2m Combine like terms: 2 + -2 = 0 -2 + 52m + 9m2 = 0 + 2m + -2m -2 + 52m + 9m2 = 2m + -2m Combine like terms: 2m + -2m = 0 -2 + 52m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + 5.777777778m + m2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 5.777777778m + 0.2222222222 + m2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 5.777777778m + m2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 5.777777778m + m2 = 0 + 0.2222222222 5.777777778m + m2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 5.777777778m + m2 = 0.2222222222 The m term is 5.777777778m. Take half its coefficient (2.888888889). Square it (8.345679013) and add it to both sides. Add '8.345679013' to each side of the equation. 5.777777778m + 8.345679013 + m2 = 0.2222222222 + 8.345679013 Reorder the terms: 8.345679013 + 5.777777778m + m2 = 0.2222222222 + 8.345679013 Combine like terms: 0.2222222222 + 8.345679013 = 8.5679012352 8.345679013 + 5.777777778m + m2 = 8.5679012352 Factor a perfect square on the left side: (m + 2.888888889)(m + 2.888888889) = 8.5679012352 Calculate the square root of the right side: 2.92709775 Break this problem into two subproblems by setting (m + 2.888888889) equal to 2.92709775 and -2.92709775.Subproblem 1
m + 2.888888889 = 2.92709775 Simplifying m + 2.888888889 = 2.92709775 Reorder the terms: 2.888888889 + m = 2.92709775 Solving 2.888888889 + m = 2.92709775 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.888888889' to each side of the equation. 2.888888889 + -2.888888889 + m = 2.92709775 + -2.888888889 Combine like terms: 2.888888889 + -2.888888889 = 0.000000000 0.000000000 + m = 2.92709775 + -2.888888889 m = 2.92709775 + -2.888888889 Combine like terms: 2.92709775 + -2.888888889 = 0.038208861 m = 0.038208861 Simplifying m = 0.038208861Subproblem 2
m + 2.888888889 = -2.92709775 Simplifying m + 2.888888889 = -2.92709775 Reorder the terms: 2.888888889 + m = -2.92709775 Solving 2.888888889 + m = -2.92709775 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.888888889' to each side of the equation. 2.888888889 + -2.888888889 + m = -2.92709775 + -2.888888889 Combine like terms: 2.888888889 + -2.888888889 = 0.000000000 0.000000000 + m = -2.92709775 + -2.888888889 m = -2.92709775 + -2.888888889 Combine like terms: -2.92709775 + -2.888888889 = -5.815986639 m = -5.815986639 Simplifying m = -5.815986639Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.038208861, -5.815986639}
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