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Simplifying 8m2 + 16m + -47 = 4 Reorder the terms: -47 + 16m + 8m2 = 4 Solving -47 + 16m + 8m2 = 4 Solving for variable 'm'. Reorder the terms: -47 + -4 + 16m + 8m2 = 4 + -4 Combine like terms: -47 + -4 = -51 -51 + 16m + 8m2 = 4 + -4 Combine like terms: 4 + -4 = 0 -51 + 16m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.375 + 2m + m2 = 0 Move the constant term to the right: Add '6.375' to each side of the equation. -6.375 + 2m + 6.375 + m2 = 0 + 6.375 Reorder the terms: -6.375 + 6.375 + 2m + m2 = 0 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + 2m + m2 = 0 + 6.375 2m + m2 = 0 + 6.375 Combine like terms: 0 + 6.375 = 6.375 2m + m2 = 6.375 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 6.375 + 1 Reorder the terms: 1 + 2m + m2 = 6.375 + 1 Combine like terms: 6.375 + 1 = 7.375 1 + 2m + m2 = 7.375 Factor a perfect square on the left side: (m + 1)(m + 1) = 7.375 Calculate the square root of the right side: 2.715695123 Break this problem into two subproblems by setting (m + 1) equal to 2.715695123 and -2.715695123.Subproblem 1
m + 1 = 2.715695123 Simplifying m + 1 = 2.715695123 Reorder the terms: 1 + m = 2.715695123 Solving 1 + m = 2.715695123 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 2.715695123 + -1 Combine like terms: 1 + -1 = 0 0 + m = 2.715695123 + -1 m = 2.715695123 + -1 Combine like terms: 2.715695123 + -1 = 1.715695123 m = 1.715695123 Simplifying m = 1.715695123Subproblem 2
m + 1 = -2.715695123 Simplifying m + 1 = -2.715695123 Reorder the terms: 1 + m = -2.715695123 Solving 1 + m = -2.715695123 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -2.715695123 + -1 Combine like terms: 1 + -1 = 0 0 + m = -2.715695123 + -1 m = -2.715695123 + -1 Combine like terms: -2.715695123 + -1 = -3.715695123 m = -3.715695123 Simplifying m = -3.715695123Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.715695123, -3.715695123}
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