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Simplifying 9m2 + -7m = 11 Reorder the terms: -7m + 9m2 = 11 Solving -7m + 9m2 = 11 Solving for variable 'm'. Reorder the terms: -11 + -7m + 9m2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -7m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.222222222 + -0.7777777778m + m2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -0.7777777778m + 1.222222222 + m2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -0.7777777778m + m2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -0.7777777778m + m2 = 0 + 1.222222222 -0.7777777778m + m2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -0.7777777778m + m2 = 1.222222222 The m term is -0.7777777778m. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778m + 0.1512345679 + m2 = 1.222222222 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778m + m2 = 1.222222222 + 0.1512345679 Combine like terms: 1.222222222 + 0.1512345679 = 1.3734567899 0.1512345679 + -0.7777777778m + m2 = 1.3734567899 Factor a perfect square on the left side: (m + -0.3888888889)(m + -0.3888888889) = 1.3734567899 Calculate the square root of the right side: 1.171945728 Break this problem into two subproblems by setting (m + -0.3888888889) equal to 1.171945728 and -1.171945728.Subproblem 1
m + -0.3888888889 = 1.171945728 Simplifying m + -0.3888888889 = 1.171945728 Reorder the terms: -0.3888888889 + m = 1.171945728 Solving -0.3888888889 + m = 1.171945728 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + m = 1.171945728 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + m = 1.171945728 + 0.3888888889 m = 1.171945728 + 0.3888888889 Combine like terms: 1.171945728 + 0.3888888889 = 1.5608346169 m = 1.5608346169 Simplifying m = 1.5608346169Subproblem 2
m + -0.3888888889 = -1.171945728 Simplifying m + -0.3888888889 = -1.171945728 Reorder the terms: -0.3888888889 + m = -1.171945728 Solving -0.3888888889 + m = -1.171945728 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + m = -1.171945728 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + m = -1.171945728 + 0.3888888889 m = -1.171945728 + 0.3888888889 Combine like terms: -1.171945728 + 0.3888888889 = -0.7830568391 m = -0.7830568391 Simplifying m = -0.7830568391Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.5608346169, -0.7830568391}
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