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Simplifying 9m2 + -3m = 8 Reorder the terms: -3m + 9m2 = 8 Solving -3m + 9m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + -3m + 9m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -3m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -0.3333333333m + m2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.3333333333m + 0.8888888889 + m2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.3333333333m + m2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.3333333333m + m2 = 0 + 0.8888888889 -0.3333333333m + m2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.3333333333m + m2 = 0.8888888889 The m term is -0.3333333333m. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333m + 0.02777777779 + m2 = 0.8888888889 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333m + m2 = 0.8888888889 + 0.02777777779 Combine like terms: 0.8888888889 + 0.02777777779 = 0.91666666669 0.02777777779 + -0.3333333333m + m2 = 0.91666666669 Factor a perfect square on the left side: (m + -0.1666666667)(m + -0.1666666667) = 0.91666666669 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (m + -0.1666666667) equal to 0.957427108 and -0.957427108.Subproblem 1
m + -0.1666666667 = 0.957427108 Simplifying m + -0.1666666667 = 0.957427108 Reorder the terms: -0.1666666667 + m = 0.957427108 Solving -0.1666666667 + m = 0.957427108 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + m = 0.957427108 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + m = 0.957427108 + 0.1666666667 m = 0.957427108 + 0.1666666667 Combine like terms: 0.957427108 + 0.1666666667 = 1.1240937747 m = 1.1240937747 Simplifying m = 1.1240937747Subproblem 2
m + -0.1666666667 = -0.957427108 Simplifying m + -0.1666666667 = -0.957427108 Reorder the terms: -0.1666666667 + m = -0.957427108 Solving -0.1666666667 + m = -0.957427108 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + m = -0.957427108 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + m = -0.957427108 + 0.1666666667 m = -0.957427108 + 0.1666666667 Combine like terms: -0.957427108 + 0.1666666667 = -0.7907604413 m = -0.7907604413 Simplifying m = -0.7907604413Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.1240937747, -0.7907604413}
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