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Simplifying 16m2 + 8m + -47 = 0 Reorder the terms: -47 + 8m + 16m2 = 0 Solving -47 + 8m + 16m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.9375 + 0.5m + m2 = 0 Move the constant term to the right: Add '2.9375' to each side of the equation. -2.9375 + 0.5m + 2.9375 + m2 = 0 + 2.9375 Reorder the terms: -2.9375 + 2.9375 + 0.5m + m2 = 0 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + 0.5m + m2 = 0 + 2.9375 0.5m + m2 = 0 + 2.9375 Combine like terms: 0 + 2.9375 = 2.9375 0.5m + m2 = 2.9375 The m term is 0.5m. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5m + 0.0625 + m2 = 2.9375 + 0.0625 Reorder the terms: 0.0625 + 0.5m + m2 = 2.9375 + 0.0625 Combine like terms: 2.9375 + 0.0625 = 3 0.0625 + 0.5m + m2 = 3 Factor a perfect square on the left side: (m + 0.25)(m + 0.25) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (m + 0.25) equal to 1.732050808 and -1.732050808.Subproblem 1
m + 0.25 = 1.732050808 Simplifying m + 0.25 = 1.732050808 Reorder the terms: 0.25 + m = 1.732050808 Solving 0.25 + m = 1.732050808 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = 1.732050808 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = 1.732050808 + -0.25 m = 1.732050808 + -0.25 Combine like terms: 1.732050808 + -0.25 = 1.482050808 m = 1.482050808 Simplifying m = 1.482050808Subproblem 2
m + 0.25 = -1.732050808 Simplifying m + 0.25 = -1.732050808 Reorder the terms: 0.25 + m = -1.732050808 Solving 0.25 + m = -1.732050808 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = -1.732050808 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = -1.732050808 + -0.25 m = -1.732050808 + -0.25 Combine like terms: -1.732050808 + -0.25 = -1.982050808 m = -1.982050808 Simplifying m = -1.982050808Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.482050808, -1.982050808}
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