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Simplifying -12m2 + 3m + 5 = 0 Reorder the terms: 5 + 3m + -12m2 = 0 Solving 5 + 3m + -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 + -0.25m + m2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.25m + 0.4166666667 + m2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.25m + m2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.25m + m2 = 0 + 0.4166666667 -0.25m + m2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.25m + m2 = 0.4166666667 The m term is -0.25m. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25m + 0.015625 + m2 = 0.4166666667 + 0.015625 Reorder the terms: 0.015625 + -0.25m + m2 = 0.4166666667 + 0.015625 Combine like terms: 0.4166666667 + 0.015625 = 0.4322916667 0.015625 + -0.25m + m2 = 0.4322916667 Factor a perfect square on the left side: (m + -0.125)(m + -0.125) = 0.4322916667 Calculate the square root of the right side: 0.65748891 Break this problem into two subproblems by setting (m + -0.125) equal to 0.65748891 and -0.65748891.Subproblem 1
m + -0.125 = 0.65748891 Simplifying m + -0.125 = 0.65748891 Reorder the terms: -0.125 + m = 0.65748891 Solving -0.125 + m = 0.65748891 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + m = 0.65748891 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + m = 0.65748891 + 0.125 m = 0.65748891 + 0.125 Combine like terms: 0.65748891 + 0.125 = 0.78248891 m = 0.78248891 Simplifying m = 0.78248891Subproblem 2
m + -0.125 = -0.65748891 Simplifying m + -0.125 = -0.65748891 Reorder the terms: -0.125 + m = -0.65748891 Solving -0.125 + m = -0.65748891 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + m = -0.65748891 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + m = -0.65748891 + 0.125 m = -0.65748891 + 0.125 Combine like terms: -0.65748891 + 0.125 = -0.53248891 m = -0.53248891 Simplifying m = -0.53248891Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.78248891, -0.53248891}
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