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Simplifying m2 + 6m + -31 = 0 Reorder the terms: -31 + 6m + m2 = 0 Solving -31 + 6m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 6m + 31 + m2 = 0 + 31 Reorder the terms: -31 + 31 + 6m + m2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 6m + m2 = 0 + 31 6m + m2 = 0 + 31 Combine like terms: 0 + 31 = 31 6m + m2 = 31 The m term is 6m. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6m + 9 + m2 = 31 + 9 Reorder the terms: 9 + 6m + m2 = 31 + 9 Combine like terms: 31 + 9 = 40 9 + 6m + m2 = 40 Factor a perfect square on the left side: (m + 3)(m + 3) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (m + 3) equal to 6.32455532 and -6.32455532.Subproblem 1
m + 3 = 6.32455532 Simplifying m + 3 = 6.32455532 Reorder the terms: 3 + m = 6.32455532 Solving 3 + m = 6.32455532 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 6.32455532 + -3 Combine like terms: 3 + -3 = 0 0 + m = 6.32455532 + -3 m = 6.32455532 + -3 Combine like terms: 6.32455532 + -3 = 3.32455532 m = 3.32455532 Simplifying m = 3.32455532Subproblem 2
m + 3 = -6.32455532 Simplifying m + 3 = -6.32455532 Reorder the terms: 3 + m = -6.32455532 Solving 3 + m = -6.32455532 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -6.32455532 + -3 Combine like terms: 3 + -3 = 0 0 + m = -6.32455532 + -3 m = -6.32455532 + -3 Combine like terms: -6.32455532 + -3 = -9.32455532 m = -9.32455532 Simplifying m = -9.32455532Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.32455532, -9.32455532}
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