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Simplifying 4m2 + 72m + -124 = 0 Reorder the terms: -124 + 72m + 4m2 = 0 Solving -124 + 72m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(-31 + 18m + m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-31 + 18m + m2)' equal to zero and attempt to solve: Simplifying -31 + 18m + m2 = 0 Solving -31 + 18m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 18m + 31 + m2 = 0 + 31 Reorder the terms: -31 + 31 + 18m + m2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 18m + m2 = 0 + 31 18m + m2 = 0 + 31 Combine like terms: 0 + 31 = 31 18m + m2 = 31 The m term is 18m. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18m + 81 + m2 = 31 + 81 Reorder the terms: 81 + 18m + m2 = 31 + 81 Combine like terms: 31 + 81 = 112 81 + 18m + m2 = 112 Factor a perfect square on the left side: (m + 9)(m + 9) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (m + 9) equal to 10.583005244 and -10.583005244.Subproblem 1
m + 9 = 10.583005244 Simplifying m + 9 = 10.583005244 Reorder the terms: 9 + m = 10.583005244 Solving 9 + m = 10.583005244 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + m = 10.583005244 + -9 Combine like terms: 9 + -9 = 0 0 + m = 10.583005244 + -9 m = 10.583005244 + -9 Combine like terms: 10.583005244 + -9 = 1.583005244 m = 1.583005244 Simplifying m = 1.583005244Subproblem 2
m + 9 = -10.583005244 Simplifying m + 9 = -10.583005244 Reorder the terms: 9 + m = -10.583005244 Solving 9 + m = -10.583005244 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + m = -10.583005244 + -9 Combine like terms: 9 + -9 = 0 0 + m = -10.583005244 + -9 m = -10.583005244 + -9 Combine like terms: -10.583005244 + -9 = -19.583005244 m = -19.583005244 Simplifying m = -19.583005244Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.583005244, -19.583005244}Solution
m = {1.583005244, -19.583005244}
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