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Simplifying m2 + 16m + 27 = 0 Reorder the terms: 27 + 16m + m2 = 0 Solving 27 + 16m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 16m + -27 + m2 = 0 + -27 Reorder the terms: 27 + -27 + 16m + m2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 16m + m2 = 0 + -27 16m + m2 = 0 + -27 Combine like terms: 0 + -27 = -27 16m + m2 = -27 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 = -27 + 64 Reorder the terms: 64 + 16m + m2 = -27 + 64 Combine like terms: -27 + 64 = 37 64 + 16m + m2 = 37 Factor a perfect square on the left side: (m + 8)(m + 8) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (m + 8) equal to 6.08276253 and -6.08276253.Subproblem 1
m + 8 = 6.08276253 Simplifying m + 8 = 6.08276253 Reorder the terms: 8 + m = 6.08276253 Solving 8 + m = 6.08276253 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 = 6.08276253 + -8 Combine like terms: 8 + -8 = 0 0 + m = 6.08276253 + -8 m = 6.08276253 + -8 Combine like terms: 6.08276253 + -8 = -1.91723747 m = -1.91723747 Simplifying m = -1.91723747Subproblem 2
m + 8 = -6.08276253 Simplifying m + 8 = -6.08276253 Reorder the terms: 8 + m = -6.08276253 Solving 8 + m = -6.08276253 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 = -6.08276253 + -8 Combine like terms: 8 + -8 = 0 0 + m = -6.08276253 + -8 m = -6.08276253 + -8 Combine like terms: -6.08276253 + -8 = -14.08276253 m = -14.08276253 Simplifying m = -14.08276253Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.91723747, -14.08276253}
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