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Simplifying 6m = 8 + -24m2 Solving 6m = 8 + -24m2 Solving for variable 'm'. Reorder the terms: -8 + 6m + 24m2 = 8 + -24m2 + -8 + 24m2 Reorder the terms: -8 + 6m + 24m2 = 8 + -8 + -24m2 + 24m2 Combine like terms: 8 + -8 = 0 -8 + 6m + 24m2 = 0 + -24m2 + 24m2 -8 + 6m + 24m2 = -24m2 + 24m2 Combine like terms: -24m2 + 24m2 = 0 -8 + 6m + 24m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3m + 12m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 3m + 12m2)' equal to zero and attempt to solve: Simplifying -4 + 3m + 12m2 = 0 Solving -4 + 3m + 12m2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + 0.25m + m2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.25m + 0.3333333333 + m2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.25m + m2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.25m + m2 = 0 + 0.3333333333 0.25m + m2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.25m + m2 = 0.3333333333 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 = 0.3333333333 + 0.015625 Reorder the terms: 0.015625 + 0.25m + m2 = 0.3333333333 + 0.015625 Combine like terms: 0.3333333333 + 0.015625 = 0.3489583333 0.015625 + 0.25m + m2 = 0.3489583333 Factor a perfect square on the left side: (m + 0.125)(m + 0.125) = 0.3489583333 Calculate the square root of the right side: 0.590726953 Break this problem into two subproblems by setting (m + 0.125) equal to 0.590726953 and -0.590726953.Subproblem 1
m + 0.125 = 0.590726953 Simplifying m + 0.125 = 0.590726953 Reorder the terms: 0.125 + m = 0.590726953 Solving 0.125 + m = 0.590726953 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 = 0.590726953 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = 0.590726953 + -0.125 m = 0.590726953 + -0.125 Combine like terms: 0.590726953 + -0.125 = 0.465726953 m = 0.465726953 Simplifying m = 0.465726953Subproblem 2
m + 0.125 = -0.590726953 Simplifying m + 0.125 = -0.590726953 Reorder the terms: 0.125 + m = -0.590726953 Solving 0.125 + m = -0.590726953 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 = -0.590726953 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = -0.590726953 + -0.125 m = -0.590726953 + -0.125 Combine like terms: -0.590726953 + -0.125 = -0.715726953 m = -0.715726953 Simplifying m = -0.715726953Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.465726953, -0.715726953}Solution
m = {0.465726953, -0.715726953}
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