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Simplifying m2 + 16m = -1 Reorder the terms: 16m + m2 = -1 Solving 16m + m2 = -1 Solving for variable 'm'. Reorder the terms: 1 + 16m + m2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 16m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + 16m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 16m + m2 = 0 + -1 16m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 16m + m2 = -1 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 = -1 + 64 Reorder the terms: 64 + 16m + m2 = -1 + 64 Combine like terms: -1 + 64 = 63 64 + 16m + m2 = 63 Factor a perfect square on the left side: (m + 8)(m + 8) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (m + 8) equal to 7.937253933 and -7.937253933.Subproblem 1
m + 8 = 7.937253933 Simplifying m + 8 = 7.937253933 Reorder the terms: 8 + m = 7.937253933 Solving 8 + m = 7.937253933 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 = 7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + m = 7.937253933 + -8 m = 7.937253933 + -8 Combine like terms: 7.937253933 + -8 = -0.062746067 m = -0.062746067 Simplifying m = -0.062746067Subproblem 2
m + 8 = -7.937253933 Simplifying m + 8 = -7.937253933 Reorder the terms: 8 + m = -7.937253933 Solving 8 + m = -7.937253933 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 = -7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + m = -7.937253933 + -8 m = -7.937253933 + -8 Combine like terms: -7.937253933 + -8 = -15.937253933 m = -15.937253933 Simplifying m = -15.937253933Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.062746067, -15.937253933}
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