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Simplifying m2 + -20m + 61 = 9 Reorder the terms: 61 + -20m + m2 = 9 Solving 61 + -20m + m2 = 9 Solving for variable 'm'. Reorder the terms: 61 + -9 + -20m + m2 = 9 + -9 Combine like terms: 61 + -9 = 52 52 + -20m + m2 = 9 + -9 Combine like terms: 9 + -9 = 0 52 + -20m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -20m + -52 + m2 = 0 + -52 Reorder the terms: 52 + -52 + -20m + m2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -20m + m2 = 0 + -52 -20m + m2 = 0 + -52 Combine like terms: 0 + -52 = -52 -20m + m2 = -52 The m term is -20m. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20m + 100 + m2 = -52 + 100 Reorder the terms: 100 + -20m + m2 = -52 + 100 Combine like terms: -52 + 100 = 48 100 + -20m + m2 = 48 Factor a perfect square on the left side: (m + -10)(m + -10) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (m + -10) equal to 6.92820323 and -6.92820323.Subproblem 1
m + -10 = 6.92820323 Simplifying m + -10 = 6.92820323 Reorder the terms: -10 + m = 6.92820323 Solving -10 + m = 6.92820323 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = 6.92820323 + 10 Combine like terms: -10 + 10 = 0 0 + m = 6.92820323 + 10 m = 6.92820323 + 10 Combine like terms: 6.92820323 + 10 = 16.92820323 m = 16.92820323 Simplifying m = 16.92820323Subproblem 2
m + -10 = -6.92820323 Simplifying m + -10 = -6.92820323 Reorder the terms: -10 + m = -6.92820323 Solving -10 + m = -6.92820323 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = -6.92820323 + 10 Combine like terms: -10 + 10 = 0 0 + m = -6.92820323 + 10 m = -6.92820323 + 10 Combine like terms: -6.92820323 + 10 = 3.07179677 m = 3.07179677 Simplifying m = 3.07179677Solution
The solution to the problem is based on the solutions from the subproblems. m = {16.92820323, 3.07179677}
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