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Simplifying 12m2 + 12m + 2 = 0 Reorder the terms: 2 + 12m + 12m2 = 0 Solving 2 + 12m + 12m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 6m + 6m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 6m + 6m2)' equal to zero and attempt to solve: Simplifying 1 + 6m + 6m2 = 0 Solving 1 + 6m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + m + m2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + m + -0.1666666667 + m2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + m + m2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + m + m2 = 0 + -0.1666666667 m + m2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 m + m2 = -0.1666666667 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = -0.1666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = -0.1666666667 + 0.25 Combine like terms: -0.1666666667 + 0.25 = 0.0833333333 1.25 + m2 = 0.0833333333 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 0.0833333333 Calculate the square root of the right side: 0.288675135 Break this problem into two subproblems by setting (m + 0.5) equal to 0.288675135 and -0.288675135.Subproblem 1
m + 0.5 = 0.288675135 Simplifying m + 0.5 = 0.288675135 Reorder the terms: 0.5 + m = 0.288675135 Solving 0.5 + m = 0.288675135 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 0.288675135 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 0.288675135 + -0.5 m = 0.288675135 + -0.5 Combine like terms: 0.288675135 + -0.5 = -0.211324865 m = -0.211324865 Simplifying m = -0.211324865Subproblem 2
m + 0.5 = -0.288675135 Simplifying m + 0.5 = -0.288675135 Reorder the terms: 0.5 + m = -0.288675135 Solving 0.5 + m = -0.288675135 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -0.288675135 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -0.288675135 + -0.5 m = -0.288675135 + -0.5 Combine like terms: -0.288675135 + -0.5 = -0.788675135 m = -0.788675135 Simplifying m = -0.788675135Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.211324865, -0.788675135}Solution
m = {-0.211324865, -0.788675135}
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