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Simplifying 2m2 + -38m = -48 Reorder the terms: -38m + 2m2 = -48 Solving -38m + 2m2 = -48 Solving for variable 'm'. Reorder the terms: 48 + -38m + 2m2 = -48 + 48 Combine like terms: -48 + 48 = 0 48 + -38m + 2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -19m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -19m + m2)' equal to zero and attempt to solve: Simplifying 24 + -19m + m2 = 0 Solving 24 + -19m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -19m + -24 + m2 = 0 + -24 Reorder the terms: 24 + -24 + -19m + m2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -19m + m2 = 0 + -24 -19m + m2 = 0 + -24 Combine like terms: 0 + -24 = -24 -19m + m2 = -24 The m term is -19m. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19m + 90.25 + m2 = -24 + 90.25 Reorder the terms: 90.25 + -19m + m2 = -24 + 90.25 Combine like terms: -24 + 90.25 = 66.25 90.25 + -19m + m2 = 66.25 Factor a perfect square on the left side: (m + -9.5)(m + -9.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (m + -9.5) equal to 8.139410298 and -8.139410298.Subproblem 1
m + -9.5 = 8.139410298 Simplifying m + -9.5 = 8.139410298 Reorder the terms: -9.5 + m = 8.139410298 Solving -9.5 + m = 8.139410298 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + m = 8.139410298 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + m = 8.139410298 + 9.5 m = 8.139410298 + 9.5 Combine like terms: 8.139410298 + 9.5 = 17.639410298 m = 17.639410298 Simplifying m = 17.639410298Subproblem 2
m + -9.5 = -8.139410298 Simplifying m + -9.5 = -8.139410298 Reorder the terms: -9.5 + m = -8.139410298 Solving -9.5 + m = -8.139410298 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + m = -8.139410298 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + m = -8.139410298 + 9.5 m = -8.139410298 + 9.5 Combine like terms: -8.139410298 + 9.5 = 1.360589702 m = 1.360589702 Simplifying m = 1.360589702Solution
The solution to the problem is based on the solutions from the subproblems. m = {17.639410298, 1.360589702}Solution
m = {17.639410298, 1.360589702}
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