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Simplifying (12m)(12m) + 11m = 15 Remove parenthesis around (12m) 12m(12m) + 11m = 15 Remove parenthesis around (12m) 12m * 12m + 11m = 15 Reorder the terms for easier multiplication: 12 * 12m * m + 11m = 15 Multiply 12 * 12 144m * m + 11m = 15 Multiply m * m 144m2 + 11m = 15 Reorder the terms: 11m + 144m2 = 15 Solving 11m + 144m2 = 15 Solving for variable 'm'. Reorder the terms: -15 + 11m + 144m2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 11m + 144m2 = 0 Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. -0.1041666667 + 0.07638888889m + m2 = 0 Move the constant term to the right: Add '0.1041666667' to each side of the equation. -0.1041666667 + 0.07638888889m + 0.1041666667 + m2 = 0 + 0.1041666667 Reorder the terms: -0.1041666667 + 0.1041666667 + 0.07638888889m + m2 = 0 + 0.1041666667 Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000 0.0000000000 + 0.07638888889m + m2 = 0 + 0.1041666667 0.07638888889m + m2 = 0 + 0.1041666667 Combine like terms: 0 + 0.1041666667 = 0.1041666667 0.07638888889m + m2 = 0.1041666667 The m term is 0.07638888889m. Take half its coefficient (0.03819444445). Square it (0.001458815587) and add it to both sides. Add '0.001458815587' to each side of the equation. 0.07638888889m + 0.001458815587 + m2 = 0.1041666667 + 0.001458815587 Reorder the terms: 0.001458815587 + 0.07638888889m + m2 = 0.1041666667 + 0.001458815587 Combine like terms: 0.1041666667 + 0.001458815587 = 0.105625482287 0.001458815587 + 0.07638888889m + m2 = 0.105625482287 Factor a perfect square on the left side: (m + 0.03819444445)(m + 0.03819444445) = 0.105625482287 Calculate the square root of the right side: 0.325000742 Break this problem into two subproblems by setting (m + 0.03819444445) equal to 0.325000742 and -0.325000742.Subproblem 1
m + 0.03819444445 = 0.325000742 Simplifying m + 0.03819444445 = 0.325000742 Reorder the terms: 0.03819444445 + m = 0.325000742 Solving 0.03819444445 + m = 0.325000742 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03819444445' to each side of the equation. 0.03819444445 + -0.03819444445 + m = 0.325000742 + -0.03819444445 Combine like terms: 0.03819444445 + -0.03819444445 = 0.00000000000 0.00000000000 + m = 0.325000742 + -0.03819444445 m = 0.325000742 + -0.03819444445 Combine like terms: 0.325000742 + -0.03819444445 = 0.28680629755 m = 0.28680629755 Simplifying m = 0.28680629755Subproblem 2
m + 0.03819444445 = -0.325000742 Simplifying m + 0.03819444445 = -0.325000742 Reorder the terms: 0.03819444445 + m = -0.325000742 Solving 0.03819444445 + m = -0.325000742 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03819444445' to each side of the equation. 0.03819444445 + -0.03819444445 + m = -0.325000742 + -0.03819444445 Combine like terms: 0.03819444445 + -0.03819444445 = 0.00000000000 0.00000000000 + m = -0.325000742 + -0.03819444445 m = -0.325000742 + -0.03819444445 Combine like terms: -0.325000742 + -0.03819444445 = -0.36319518645 m = -0.36319518645 Simplifying m = -0.36319518645Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.28680629755, -0.36319518645}
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