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Simplifying (11m2 + 2m + -6) + -1(4m2 + m + -1) = 0 Reorder the terms: (-6 + 2m + 11m2) + -1(4m2 + m + -1) = 0 Remove parenthesis around (-6 + 2m + 11m2) -6 + 2m + 11m2 + -1(4m2 + m + -1) = 0 Reorder the terms: -6 + 2m + 11m2 + -1(-1 + m + 4m2) = 0 -6 + 2m + 11m2 + (-1 * -1 + m * -1 + 4m2 * -1) = 0 -6 + 2m + 11m2 + (1 + -1m + -4m2) = 0 Reorder the terms: -6 + 1 + 2m + -1m + 11m2 + -4m2 = 0 Combine like terms: -6 + 1 = -5 -5 + 2m + -1m + 11m2 + -4m2 = 0 Combine like terms: 2m + -1m = 1m -5 + 1m + 11m2 + -4m2 = 0 Combine like terms: 11m2 + -4m2 = 7m2 -5 + 1m + 7m2 = 0 Solving -5 + 1m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 0.1428571429m + m2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.1428571429m + 0.7142857143 + m2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.1428571429m + m2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.1428571429m + m2 = 0 + 0.7142857143 0.1428571429m + m2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.1428571429m + m2 = 0.7142857143 The m term is 0.1428571429m. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429m + 0.005102040819 + m2 = 0.7142857143 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429m + m2 = 0.7142857143 + 0.005102040819 Combine like terms: 0.7142857143 + 0.005102040819 = 0.719387755119 0.005102040819 + 0.1428571429m + m2 = 0.719387755119 Factor a perfect square on the left side: (m + 0.07142857145)(m + 0.07142857145) = 0.719387755119 Calculate the square root of the right side: 0.848167292 Break this problem into two subproblems by setting (m + 0.07142857145) equal to 0.848167292 and -0.848167292.Subproblem 1
m + 0.07142857145 = 0.848167292 Simplifying m + 0.07142857145 = 0.848167292 Reorder the terms: 0.07142857145 + m = 0.848167292 Solving 0.07142857145 + m = 0.848167292 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + m = 0.848167292 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + m = 0.848167292 + -0.07142857145 m = 0.848167292 + -0.07142857145 Combine like terms: 0.848167292 + -0.07142857145 = 0.77673872055 m = 0.77673872055 Simplifying m = 0.77673872055Subproblem 2
m + 0.07142857145 = -0.848167292 Simplifying m + 0.07142857145 = -0.848167292 Reorder the terms: 0.07142857145 + m = -0.848167292 Solving 0.07142857145 + m = -0.848167292 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + m = -0.848167292 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + m = -0.848167292 + -0.07142857145 m = -0.848167292 + -0.07142857145 Combine like terms: -0.848167292 + -0.07142857145 = -0.91959586345 m = -0.91959586345 Simplifying m = -0.91959586345Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.77673872055, -0.91959586345}
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