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Simplifying m2 + 9m + 10 = 0 Reorder the terms: 10 + 9m + m2 = 0 Solving 10 + 9m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 9m + -10 + m2 = 0 + -10 Reorder the terms: 10 + -10 + 9m + m2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 9m + m2 = 0 + -10 9m + m2 = 0 + -10 Combine like terms: 0 + -10 = -10 9m + m2 = -10 The m term is 9m. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9m + 20.25 + m2 = -10 + 20.25 Reorder the terms: 20.25 + 9m + m2 = -10 + 20.25 Combine like terms: -10 + 20.25 = 10.25 20.25 + 9m + m2 = 10.25 Factor a perfect square on the left side: (m + 4.5)(m + 4.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (m + 4.5) equal to 3.201562119 and -3.201562119.Subproblem 1
m + 4.5 = 3.201562119 Simplifying m + 4.5 = 3.201562119 Reorder the terms: 4.5 + m = 3.201562119 Solving 4.5 + m = 3.201562119 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + m = 3.201562119 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + m = 3.201562119 + -4.5 m = 3.201562119 + -4.5 Combine like terms: 3.201562119 + -4.5 = -1.298437881 m = -1.298437881 Simplifying m = -1.298437881Subproblem 2
m + 4.5 = -3.201562119 Simplifying m + 4.5 = -3.201562119 Reorder the terms: 4.5 + m = -3.201562119 Solving 4.5 + m = -3.201562119 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + m = -3.201562119 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + m = -3.201562119 + -4.5 m = -3.201562119 + -4.5 Combine like terms: -3.201562119 + -4.5 = -7.701562119 m = -7.701562119 Simplifying m = -7.701562119Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.298437881, -7.701562119}
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