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Simplifying 6m(8 + -1m) = 2 + m (8 * 6m + -1m * 6m) = 2 + m (48m + -6m2) = 2 + m Solving 48m + -6m2 = 2 + m Solving for variable 'm'. Reorder the terms: -2 + 48m + -1m + -6m2 = 2 + m + -2 + -1m Combine like terms: 48m + -1m = 47m -2 + 47m + -6m2 = 2 + m + -2 + -1m Reorder the terms: -2 + 47m + -6m2 = 2 + -2 + m + -1m Combine like terms: 2 + -2 = 0 -2 + 47m + -6m2 = 0 + m + -1m -2 + 47m + -6m2 = m + -1m Combine like terms: m + -1m = 0 -2 + 47m + -6m2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.3333333333 + -7.833333333m + m2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -7.833333333m + -0.3333333333 + m2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -7.833333333m + m2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -7.833333333m + m2 = 0 + -0.3333333333 -7.833333333m + m2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -7.833333333m + m2 = -0.3333333333 The m term is -7.833333333m. Take half its coefficient (-3.916666667). Square it (15.34027778) and add it to both sides. Add '15.34027778' to each side of the equation. -7.833333333m + 15.34027778 + m2 = -0.3333333333 + 15.34027778 Reorder the terms: 15.34027778 + -7.833333333m + m2 = -0.3333333333 + 15.34027778 Combine like terms: -0.3333333333 + 15.34027778 = 15.0069444467 15.34027778 + -7.833333333m + m2 = 15.0069444467 Factor a perfect square on the left side: (m + -3.916666667)(m + -3.916666667) = 15.0069444467 Calculate the square root of the right side: 3.873879767 Break this problem into two subproblems by setting (m + -3.916666667) equal to 3.873879767 and -3.873879767.Subproblem 1
m + -3.916666667 = 3.873879767 Simplifying m + -3.916666667 = 3.873879767 Reorder the terms: -3.916666667 + m = 3.873879767 Solving -3.916666667 + m = 3.873879767 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + m = 3.873879767 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + m = 3.873879767 + 3.916666667 m = 3.873879767 + 3.916666667 Combine like terms: 3.873879767 + 3.916666667 = 7.790546434 m = 7.790546434 Simplifying m = 7.790546434Subproblem 2
m + -3.916666667 = -3.873879767 Simplifying m + -3.916666667 = -3.873879767 Reorder the terms: -3.916666667 + m = -3.873879767 Solving -3.916666667 + m = -3.873879767 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + m = -3.873879767 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + m = -3.873879767 + 3.916666667 m = -3.873879767 + 3.916666667 Combine like terms: -3.873879767 + 3.916666667 = 0.0427869 m = 0.0427869 Simplifying m = 0.0427869Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.790546434, 0.0427869}
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