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Simplifying 60m2 + 240m + 24 = 0 Reorder the terms: 24 + 240m + 60m2 = 0 Solving 24 + 240m + 60m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '12'. 12(2 + 20m + 5m2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(2 + 20m + 5m2)' equal to zero and attempt to solve: Simplifying 2 + 20m + 5m2 = 0 Solving 2 + 20m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 4m + m2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 4m + -0.4 + m2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 4m + m2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 4m + m2 = 0 + -0.4 4m + m2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 4m + m2 = -0.4 The m term is 4m. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m + 4 + m2 = -0.4 + 4 Reorder the terms: 4 + 4m + m2 = -0.4 + 4 Combine like terms: -0.4 + 4 = 3.6 4 + 4m + m2 = 3.6 Factor a perfect square on the left side: (m + 2)(m + 2) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (m + 2) equal to 1.897366596 and -1.897366596.Subproblem 1
m + 2 = 1.897366596 Simplifying m + 2 = 1.897366596 Reorder the terms: 2 + m = 1.897366596 Solving 2 + m = 1.897366596 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 1.897366596 + -2 Combine like terms: 2 + -2 = 0 0 + m = 1.897366596 + -2 m = 1.897366596 + -2 Combine like terms: 1.897366596 + -2 = -0.102633404 m = -0.102633404 Simplifying m = -0.102633404Subproblem 2
m + 2 = -1.897366596 Simplifying m + 2 = -1.897366596 Reorder the terms: 2 + m = -1.897366596 Solving 2 + m = -1.897366596 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = -1.897366596 + -2 Combine like terms: 2 + -2 = 0 0 + m = -1.897366596 + -2 m = -1.897366596 + -2 Combine like terms: -1.897366596 + -2 = -3.897366596 m = -3.897366596 Simplifying m = -3.897366596Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.102633404, -3.897366596}Solution
m = {-0.102633404, -3.897366596}
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