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Simplifying 9m2 + -72m + 8 = 0 Reorder the terms: 8 + -72m + 9m2 = 0 Solving 8 + -72m + 9m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + -8m + m2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + -8m + -0.8888888889 + m2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + -8m + m2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + -8m + m2 = 0 + -0.8888888889 -8m + m2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 -8m + m2 = -0.8888888889 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = -0.8888888889 + 16 Reorder the terms: 16 + -8m + m2 = -0.8888888889 + 16 Combine like terms: -0.8888888889 + 16 = 15.1111111111 16 + -8m + m2 = 15.1111111111 Factor a perfect square on the left side: (m + -4)(m + -4) = 15.1111111111 Calculate the square root of the right side: 3.887301263 Break this problem into two subproblems by setting (m + -4) equal to 3.887301263 and -3.887301263.Subproblem 1
m + -4 = 3.887301263 Simplifying m + -4 = 3.887301263 Reorder the terms: -4 + m = 3.887301263 Solving -4 + m = 3.887301263 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 3.887301263 + 4 Combine like terms: -4 + 4 = 0 0 + m = 3.887301263 + 4 m = 3.887301263 + 4 Combine like terms: 3.887301263 + 4 = 7.887301263 m = 7.887301263 Simplifying m = 7.887301263Subproblem 2
m + -4 = -3.887301263 Simplifying m + -4 = -3.887301263 Reorder the terms: -4 + m = -3.887301263 Solving -4 + m = -3.887301263 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -3.887301263 + 4 Combine like terms: -4 + 4 = 0 0 + m = -3.887301263 + 4 m = -3.887301263 + 4 Combine like terms: -3.887301263 + 4 = 0.112698737 m = 0.112698737 Simplifying m = 0.112698737Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.887301263, 0.112698737}
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