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Simplifying -6m(8m + -7) = -246 Reorder the terms: -6m(-7 + 8m) = -246 (-7 * -6m + 8m * -6m) = -246 (42m + -48m2) = -246 Solving 42m + -48m2 = -246 Solving for variable 'm'. Reorder the terms: 246 + 42m + -48m2 = -246 + 246 Combine like terms: -246 + 246 = 0 246 + 42m + -48m2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(41 + 7m + -8m2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(41 + 7m + -8m2)' equal to zero and attempt to solve: Simplifying 41 + 7m + -8m2 = 0 Solving 41 + 7m + -8m2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -5.125 + -0.875m + m2 = 0 Move the constant term to the right: Add '5.125' to each side of the equation. -5.125 + -0.875m + 5.125 + m2 = 0 + 5.125 Reorder the terms: -5.125 + 5.125 + -0.875m + m2 = 0 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + -0.875m + m2 = 0 + 5.125 -0.875m + m2 = 0 + 5.125 Combine like terms: 0 + 5.125 = 5.125 -0.875m + m2 = 5.125 The m term is -0.875m. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875m + 0.19140625 + m2 = 5.125 + 0.19140625 Reorder the terms: 0.19140625 + -0.875m + m2 = 5.125 + 0.19140625 Combine like terms: 5.125 + 0.19140625 = 5.31640625 0.19140625 + -0.875m + m2 = 5.31640625 Factor a perfect square on the left side: (m + -0.4375)(m + -0.4375) = 5.31640625 Calculate the square root of the right side: 2.305733343 Break this problem into two subproblems by setting (m + -0.4375) equal to 2.305733343 and -2.305733343.Subproblem 1
m + -0.4375 = 2.305733343 Simplifying m + -0.4375 = 2.305733343 Reorder the terms: -0.4375 + m = 2.305733343 Solving -0.4375 + m = 2.305733343 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = 2.305733343 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = 2.305733343 + 0.4375 m = 2.305733343 + 0.4375 Combine like terms: 2.305733343 + 0.4375 = 2.743233343 m = 2.743233343 Simplifying m = 2.743233343Subproblem 2
m + -0.4375 = -2.305733343 Simplifying m + -0.4375 = -2.305733343 Reorder the terms: -0.4375 + m = -2.305733343 Solving -0.4375 + m = -2.305733343 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = -2.305733343 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = -2.305733343 + 0.4375 m = -2.305733343 + 0.4375 Combine like terms: -2.305733343 + 0.4375 = -1.868233343 m = -1.868233343 Simplifying m = -1.868233343Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.743233343, -1.868233343}Solution
m = {2.743233343, -1.868233343}
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