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Simplifying 39m2 + -14m + -99 = 0 Reorder the terms: -99 + -14m + 39m2 = 0 Solving -99 + -14m + 39m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -2.538461538 + -0.358974359m + m2 = 0 Move the constant term to the right: Add '2.538461538' to each side of the equation. -2.538461538 + -0.358974359m + 2.538461538 + m2 = 0 + 2.538461538 Reorder the terms: -2.538461538 + 2.538461538 + -0.358974359m + m2 = 0 + 2.538461538 Combine like terms: -2.538461538 + 2.538461538 = 0.000000000 0.000000000 + -0.358974359m + m2 = 0 + 2.538461538 -0.358974359m + m2 = 0 + 2.538461538 Combine like terms: 0 + 2.538461538 = 2.538461538 -0.358974359m + m2 = 2.538461538 The m term is -0.358974359m. Take half its coefficient (-0.1794871795). Square it (0.03221564760) and add it to both sides. Add '0.03221564760' to each side of the equation. -0.358974359m + 0.03221564760 + m2 = 2.538461538 + 0.03221564760 Reorder the terms: 0.03221564760 + -0.358974359m + m2 = 2.538461538 + 0.03221564760 Combine like terms: 2.538461538 + 0.03221564760 = 2.5706771856 0.03221564760 + -0.358974359m + m2 = 2.5706771856 Factor a perfect square on the left side: (m + -0.1794871795)(m + -0.1794871795) = 2.5706771856 Calculate the square root of the right side: 1.603333149 Break this problem into two subproblems by setting (m + -0.1794871795) equal to 1.603333149 and -1.603333149.Subproblem 1
m + -0.1794871795 = 1.603333149 Simplifying m + -0.1794871795 = 1.603333149 Reorder the terms: -0.1794871795 + m = 1.603333149 Solving -0.1794871795 + m = 1.603333149 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1794871795' to each side of the equation. -0.1794871795 + 0.1794871795 + m = 1.603333149 + 0.1794871795 Combine like terms: -0.1794871795 + 0.1794871795 = 0.0000000000 0.0000000000 + m = 1.603333149 + 0.1794871795 m = 1.603333149 + 0.1794871795 Combine like terms: 1.603333149 + 0.1794871795 = 1.7828203285 m = 1.7828203285 Simplifying m = 1.7828203285Subproblem 2
m + -0.1794871795 = -1.603333149 Simplifying m + -0.1794871795 = -1.603333149 Reorder the terms: -0.1794871795 + m = -1.603333149 Solving -0.1794871795 + m = -1.603333149 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1794871795' to each side of the equation. -0.1794871795 + 0.1794871795 + m = -1.603333149 + 0.1794871795 Combine like terms: -0.1794871795 + 0.1794871795 = 0.0000000000 0.0000000000 + m = -1.603333149 + 0.1794871795 m = -1.603333149 + 0.1794871795 Combine like terms: -1.603333149 + 0.1794871795 = -1.4238459695 m = -1.4238459695 Simplifying m = -1.4238459695Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.7828203285, -1.4238459695}
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