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Simplifying m2 + 18m + 77 = 3 Reorder the terms: 77 + 18m + m2 = 3 Solving 77 + 18m + m2 = 3 Solving for variable 'm'. Reorder the terms: 77 + -3 + 18m + m2 = 3 + -3 Combine like terms: 77 + -3 = 74 74 + 18m + m2 = 3 + -3 Combine like terms: 3 + -3 = 0 74 + 18m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-74' to each side of the equation. 74 + 18m + -74 + m2 = 0 + -74 Reorder the terms: 74 + -74 + 18m + m2 = 0 + -74 Combine like terms: 74 + -74 = 0 0 + 18m + m2 = 0 + -74 18m + m2 = 0 + -74 Combine like terms: 0 + -74 = -74 18m + m2 = -74 The m term is 18m. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18m + 81 + m2 = -74 + 81 Reorder the terms: 81 + 18m + m2 = -74 + 81 Combine like terms: -74 + 81 = 7 81 + 18m + m2 = 7 Factor a perfect square on the left side: (m + 9)(m + 9) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (m + 9) equal to 2.645751311 and -2.645751311.Subproblem 1
m + 9 = 2.645751311 Simplifying m + 9 = 2.645751311 Reorder the terms: 9 + m = 2.645751311 Solving 9 + m = 2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + m = 2.645751311 + -9 Combine like terms: 9 + -9 = 0 0 + m = 2.645751311 + -9 m = 2.645751311 + -9 Combine like terms: 2.645751311 + -9 = -6.354248689 m = -6.354248689 Simplifying m = -6.354248689Subproblem 2
m + 9 = -2.645751311 Simplifying m + 9 = -2.645751311 Reorder the terms: 9 + m = -2.645751311 Solving 9 + m = -2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + m = -2.645751311 + -9 Combine like terms: 9 + -9 = 0 0 + m = -2.645751311 + -9 m = -2.645751311 + -9 Combine like terms: -2.645751311 + -9 = -11.645751311 m = -11.645751311 Simplifying m = -11.645751311Solution
The solution to the problem is based on the solutions from the subproblems. m = {-6.354248689, -11.645751311}
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