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Simplifying m2 + 18m + 4 = 6 Reorder the terms: 4 + 18m + m2 = 6 Solving 4 + 18m + m2 = 6 Solving for variable 'm'. Reorder the terms: 4 + -6 + 18m + m2 = 6 + -6 Combine like terms: 4 + -6 = -2 -2 + 18m + m2 = 6 + -6 Combine like terms: 6 + -6 = 0 -2 + 18m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 18m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + 18m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 18m + m2 = 0 + 2 18m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 18m + m2 = 2 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 = 2 + 81 Reorder the terms: 81 + 18m + m2 = 2 + 81 Combine like terms: 2 + 81 = 83 81 + 18m + m2 = 83 Factor a perfect square on the left side: (m + 9)(m + 9) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (m + 9) equal to 9.110433579 and -9.110433579.Subproblem 1
m + 9 = 9.110433579 Simplifying m + 9 = 9.110433579 Reorder the terms: 9 + m = 9.110433579 Solving 9 + m = 9.110433579 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 = 9.110433579 + -9 Combine like terms: 9 + -9 = 0 0 + m = 9.110433579 + -9 m = 9.110433579 + -9 Combine like terms: 9.110433579 + -9 = 0.110433579 m = 0.110433579 Simplifying m = 0.110433579Subproblem 2
m + 9 = -9.110433579 Simplifying m + 9 = -9.110433579 Reorder the terms: 9 + m = -9.110433579 Solving 9 + m = -9.110433579 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 = -9.110433579 + -9 Combine like terms: 9 + -9 = 0 0 + m = -9.110433579 + -9 m = -9.110433579 + -9 Combine like terms: -9.110433579 + -9 = -18.110433579 m = -18.110433579 Simplifying m = -18.110433579Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.110433579, -18.110433579}
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