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Simplifying 12m2 + 18m + 5 = 0 Reorder the terms: 5 + 18m + 12m2 = 0 Solving 5 + 18m + 12m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + 1.5m + m2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 1.5m + -0.4166666667 + m2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 1.5m + m2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 1.5m + m2 = 0 + -0.4166666667 1.5m + m2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 1.5m + m2 = -0.4166666667 The m term is 1.5m. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5m + 0.5625 + m2 = -0.4166666667 + 0.5625 Reorder the terms: 0.5625 + 1.5m + m2 = -0.4166666667 + 0.5625 Combine like terms: -0.4166666667 + 0.5625 = 0.1458333333 0.5625 + 1.5m + m2 = 0.1458333333 Factor a perfect square on the left side: (m + 0.75)(m + 0.75) = 0.1458333333 Calculate the square root of the right side: 0.381881308 Break this problem into two subproblems by setting (m + 0.75) equal to 0.381881308 and -0.381881308.Subproblem 1
m + 0.75 = 0.381881308 Simplifying m + 0.75 = 0.381881308 Reorder the terms: 0.75 + m = 0.381881308 Solving 0.75 + m = 0.381881308 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m = 0.381881308 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m = 0.381881308 + -0.75 m = 0.381881308 + -0.75 Combine like terms: 0.381881308 + -0.75 = -0.368118692 m = -0.368118692 Simplifying m = -0.368118692Subproblem 2
m + 0.75 = -0.381881308 Simplifying m + 0.75 = -0.381881308 Reorder the terms: 0.75 + m = -0.381881308 Solving 0.75 + m = -0.381881308 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m = -0.381881308 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m = -0.381881308 + -0.75 m = -0.381881308 + -0.75 Combine like terms: -0.381881308 + -0.75 = -1.131881308 m = -1.131881308 Simplifying m = -1.131881308Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.368118692, -1.131881308}
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