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Simplifying m2 + 16m + -59 = 0 Reorder the terms: -59 + 16m + m2 = 0 Solving -59 + 16m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 16m + 59 + m2 = 0 + 59 Reorder the terms: -59 + 59 + 16m + m2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 16m + m2 = 0 + 59 16m + m2 = 0 + 59 Combine like terms: 0 + 59 = 59 16m + m2 = 59 The m term is 16m. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16m + 64 + m2 = 59 + 64 Reorder the terms: 64 + 16m + m2 = 59 + 64 Combine like terms: 59 + 64 = 123 64 + 16m + m2 = 123 Factor a perfect square on the left side: (m + 8)(m + 8) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (m + 8) equal to 11.090536506 and -11.090536506.Subproblem 1
m + 8 = 11.090536506 Simplifying m + 8 = 11.090536506 Reorder the terms: 8 + m = 11.090536506 Solving 8 + m = 11.090536506 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = 11.090536506 + -8 Combine like terms: 8 + -8 = 0 0 + m = 11.090536506 + -8 m = 11.090536506 + -8 Combine like terms: 11.090536506 + -8 = 3.090536506 m = 3.090536506 Simplifying m = 3.090536506Subproblem 2
m + 8 = -11.090536506 Simplifying m + 8 = -11.090536506 Reorder the terms: 8 + m = -11.090536506 Solving 8 + m = -11.090536506 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + m = -11.090536506 + -8 Combine like terms: 8 + -8 = 0 0 + m = -11.090536506 + -8 m = -11.090536506 + -8 Combine like terms: -11.090536506 + -8 = -19.090536506 m = -19.090536506 Simplifying m = -19.090536506Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.090536506, -19.090536506}
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