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Simplifying 102b + b2 = 3 Solving 102b + b2 = 3 Solving for variable 'b'. Reorder the terms: -3 + 102b + b2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 102b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 102b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + 102b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 102b + b2 = 0 + 3 102b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 102b + b2 = 3 The b term is 102b. Take half its coefficient (51). Square it (2601) and add it to both sides. Add '2601' to each side of the equation. 102b + 2601 + b2 = 3 + 2601 Reorder the terms: 2601 + 102b + b2 = 3 + 2601 Combine like terms: 3 + 2601 = 2604 2601 + 102b + b2 = 2604 Factor a perfect square on the left side: (b + 51)(b + 51) = 2604 Calculate the square root of the right side: 51.029403289 Break this problem into two subproblems by setting (b + 51) equal to 51.029403289 and -51.029403289.Subproblem 1
b + 51 = 51.029403289 Simplifying b + 51 = 51.029403289 Reorder the terms: 51 + b = 51.029403289 Solving 51 + b = 51.029403289 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-51' to each side of the equation. 51 + -51 + b = 51.029403289 + -51 Combine like terms: 51 + -51 = 0 0 + b = 51.029403289 + -51 b = 51.029403289 + -51 Combine like terms: 51.029403289 + -51 = 0.029403289 b = 0.029403289 Simplifying b = 0.029403289Subproblem 2
b + 51 = -51.029403289 Simplifying b + 51 = -51.029403289 Reorder the terms: 51 + b = -51.029403289 Solving 51 + b = -51.029403289 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-51' to each side of the equation. 51 + -51 + b = -51.029403289 + -51 Combine like terms: 51 + -51 = 0 0 + b = -51.029403289 + -51 b = -51.029403289 + -51 Combine like terms: -51.029403289 + -51 = -102.029403289 b = -102.029403289 Simplifying b = -102.029403289Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.029403289, -102.029403289}
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