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Simplifying 9m(m + -2) = m + 40 Reorder the terms: 9m(-2 + m) = m + 40 (-2 * 9m + m * 9m) = m + 40 (-18m + 9m2) = m + 40 Reorder the terms: -18m + 9m2 = 40 + m Solving -18m + 9m2 = 40 + m Solving for variable 'm'. Reorder the terms: -40 + -18m + -1m + 9m2 = 40 + m + -40 + -1m Combine like terms: -18m + -1m = -19m -40 + -19m + 9m2 = 40 + m + -40 + -1m Reorder the terms: -40 + -19m + 9m2 = 40 + -40 + m + -1m Combine like terms: 40 + -40 = 0 -40 + -19m + 9m2 = 0 + m + -1m -40 + -19m + 9m2 = m + -1m Combine like terms: m + -1m = 0 -40 + -19m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.444444444 + -2.111111111m + m2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + -2.111111111m + 4.444444444 + m2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + -2.111111111m + m2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + -2.111111111m + m2 = 0 + 4.444444444 -2.111111111m + m2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 -2.111111111m + m2 = 4.444444444 The m term is -2.111111111m. Take half its coefficient (-1.055555556). Square it (1.114197532) and add it to both sides. Add '1.114197532' to each side of the equation. -2.111111111m + 1.114197532 + m2 = 4.444444444 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111m + m2 = 4.444444444 + 1.114197532 Combine like terms: 4.444444444 + 1.114197532 = 5.558641976 1.114197532 + -2.111111111m + m2 = 5.558641976 Factor a perfect square on the left side: (m + -1.055555556)(m + -1.055555556) = 5.558641976 Calculate the square root of the right side: 2.357677242 Break this problem into two subproblems by setting (m + -1.055555556) equal to 2.357677242 and -2.357677242.Subproblem 1
m + -1.055555556 = 2.357677242 Simplifying m + -1.055555556 = 2.357677242 Reorder the terms: -1.055555556 + m = 2.357677242 Solving -1.055555556 + m = 2.357677242 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + m = 2.357677242 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + m = 2.357677242 + 1.055555556 m = 2.357677242 + 1.055555556 Combine like terms: 2.357677242 + 1.055555556 = 3.413232798 m = 3.413232798 Simplifying m = 3.413232798Subproblem 2
m + -1.055555556 = -2.357677242 Simplifying m + -1.055555556 = -2.357677242 Reorder the terms: -1.055555556 + m = -2.357677242 Solving -1.055555556 + m = -2.357677242 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + m = -2.357677242 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + m = -2.357677242 + 1.055555556 m = -2.357677242 + 1.055555556 Combine like terms: -2.357677242 + 1.055555556 = -1.302121686 m = -1.302121686 Simplifying m = -1.302121686Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.413232798, -1.302121686}
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