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Simplifying m2 + -16m + 16 = -2 Reorder the terms: 16 + -16m + m2 = -2 Solving 16 + -16m + m2 = -2 Solving for variable 'm'. Reorder the terms: 16 + 2 + -16m + m2 = -2 + 2 Combine like terms: 16 + 2 = 18 18 + -16m + m2 = -2 + 2 Combine like terms: -2 + 2 = 0 18 + -16m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -16m + -18 + m2 = 0 + -18 Reorder the terms: 18 + -18 + -16m + m2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -16m + m2 = 0 + -18 -16m + m2 = 0 + -18 Combine like terms: 0 + -18 = -18 -16m + m2 = -18 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 = -18 + 64 Reorder the terms: 64 + -16m + m2 = -18 + 64 Combine like terms: -18 + 64 = 46 64 + -16m + m2 = 46 Factor a perfect square on the left side: (m + -8)(m + -8) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (m + -8) equal to 6.782329983 and -6.782329983.Subproblem 1
m + -8 = 6.782329983 Simplifying m + -8 = 6.782329983 Reorder the terms: -8 + m = 6.782329983 Solving -8 + m = 6.782329983 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 = 6.782329983 + 8 Combine like terms: -8 + 8 = 0 0 + m = 6.782329983 + 8 m = 6.782329983 + 8 Combine like terms: 6.782329983 + 8 = 14.782329983 m = 14.782329983 Simplifying m = 14.782329983Subproblem 2
m + -8 = -6.782329983 Simplifying m + -8 = -6.782329983 Reorder the terms: -8 + m = -6.782329983 Solving -8 + m = -6.782329983 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 = -6.782329983 + 8 Combine like terms: -8 + 8 = 0 0 + m = -6.782329983 + 8 m = -6.782329983 + 8 Combine like terms: -6.782329983 + 8 = 1.217670017 m = 1.217670017 Simplifying m = 1.217670017Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.782329983, 1.217670017}
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