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Simplifying (m + 4)(m + 1) = 9 Reorder the terms: (4 + m)(m + 1) = 9 Reorder the terms: (4 + m)(1 + m) = 9 Multiply (4 + m) * (1 + m) (4(1 + m) + m(1 + m)) = 9 ((1 * 4 + m * 4) + m(1 + m)) = 9 ((4 + 4m) + m(1 + m)) = 9 (4 + 4m + (1 * m + m * m)) = 9 (4 + 4m + (1m + m2)) = 9 Combine like terms: 4m + 1m = 5m (4 + 5m + m2) = 9 Solving 4 + 5m + m2 = 9 Solving for variable 'm'. Reorder the terms: 4 + -9 + 5m + m2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + 5m + m2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + 5m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 5m + 5 + m2 = 0 + 5 Reorder the terms: -5 + 5 + 5m + m2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5m + m2 = 0 + 5 5m + m2 = 0 + 5 Combine like terms: 0 + 5 = 5 5m + m2 = 5 The m term is 5m. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5m + 6.25 + m2 = 5 + 6.25 Reorder the terms: 6.25 + 5m + m2 = 5 + 6.25 Combine like terms: 5 + 6.25 = 11.25 6.25 + 5m + m2 = 11.25 Factor a perfect square on the left side: (m + 2.5)(m + 2.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (m + 2.5) equal to 3.354101966 and -3.354101966.Subproblem 1
m + 2.5 = 3.354101966 Simplifying m + 2.5 = 3.354101966 Reorder the terms: 2.5 + m = 3.354101966 Solving 2.5 + m = 3.354101966 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = 3.354101966 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = 3.354101966 + -2.5 m = 3.354101966 + -2.5 Combine like terms: 3.354101966 + -2.5 = 0.854101966 m = 0.854101966 Simplifying m = 0.854101966Subproblem 2
m + 2.5 = -3.354101966 Simplifying m + 2.5 = -3.354101966 Reorder the terms: 2.5 + m = -3.354101966 Solving 2.5 + m = -3.354101966 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = -3.354101966 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = -3.354101966 + -2.5 m = -3.354101966 + -2.5 Combine like terms: -3.354101966 + -2.5 = -5.854101966 m = -5.854101966 Simplifying m = -5.854101966Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.854101966, -5.854101966}
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