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Simplifying m2 + 16m + 47 = 6 Reorder the terms: 47 + 16m + m2 = 6 Solving 47 + 16m + m2 = 6 Solving for variable 'm'. Reorder the terms: 47 + -6 + 16m + m2 = 6 + -6 Combine like terms: 47 + -6 = 41 41 + 16m + m2 = 6 + -6 Combine like terms: 6 + -6 = 0 41 + 16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 16m + -41 + m2 = 0 + -41 Reorder the terms: 41 + -41 + 16m + m2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 16m + m2 = 0 + -41 16m + m2 = 0 + -41 Combine like terms: 0 + -41 = -41 16m + m2 = -41 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 = -41 + 64 Reorder the terms: 64 + 16m + m2 = -41 + 64 Combine like terms: -41 + 64 = 23 64 + 16m + m2 = 23 Factor a perfect square on the left side: (m + 8)(m + 8) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (m + 8) equal to 4.795831523 and -4.795831523.Subproblem 1
m + 8 = 4.795831523 Simplifying m + 8 = 4.795831523 Reorder the terms: 8 + m = 4.795831523 Solving 8 + m = 4.795831523 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 = 4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + m = 4.795831523 + -8 m = 4.795831523 + -8 Combine like terms: 4.795831523 + -8 = -3.204168477 m = -3.204168477 Simplifying m = -3.204168477Subproblem 2
m + 8 = -4.795831523 Simplifying m + 8 = -4.795831523 Reorder the terms: 8 + m = -4.795831523 Solving 8 + m = -4.795831523 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 = -4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + m = -4.795831523 + -8 m = -4.795831523 + -8 Combine like terms: -4.795831523 + -8 = -12.795831523 m = -12.795831523 Simplifying m = -12.795831523Solution
The solution to the problem is based on the solutions from the subproblems. m = {-3.204168477, -12.795831523}
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