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Simplifying 6m2 + 12m + 2 = 0 Reorder the terms: 2 + 12m + 6m2 = 0 Solving 2 + 12m + 6m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 6m + 3m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 6m + 3m2)' equal to zero and attempt to solve: Simplifying 1 + 6m + 3m2 = 0 Solving 1 + 6m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 2m + m2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 2m + -0.3333333333 + m2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 2m + m2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 2m + m2 = 0 + -0.3333333333 2m + m2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 2m + m2 = -0.3333333333 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = -0.3333333333 + 1 Reorder the terms: 1 + 2m + m2 = -0.3333333333 + 1 Combine like terms: -0.3333333333 + 1 = 0.6666666667 1 + 2m + m2 = 0.6666666667 Factor a perfect square on the left side: (m + 1)(m + 1) = 0.6666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (m + 1) equal to 0.816496581 and -0.816496581.Subproblem 1
m + 1 = 0.816496581 Simplifying m + 1 = 0.816496581 Reorder the terms: 1 + m = 0.816496581 Solving 1 + m = 0.816496581 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 0.816496581 + -1 Combine like terms: 1 + -1 = 0 0 + m = 0.816496581 + -1 m = 0.816496581 + -1 Combine like terms: 0.816496581 + -1 = -0.183503419 m = -0.183503419 Simplifying m = -0.183503419Subproblem 2
m + 1 = -0.816496581 Simplifying m + 1 = -0.816496581 Reorder the terms: 1 + m = -0.816496581 Solving 1 + m = -0.816496581 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -0.816496581 + -1 Combine like terms: 1 + -1 = 0 0 + m = -0.816496581 + -1 m = -0.816496581 + -1 Combine like terms: -0.816496581 + -1 = -1.816496581 m = -1.816496581 Simplifying m = -1.816496581Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.183503419, -1.816496581}Solution
m = {-0.183503419, -1.816496581}
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