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Simplifying 16b2 + -25 = b + 25 Reorder the terms: -25 + 16b2 = b + 25 Reorder the terms: -25 + 16b2 = 25 + b Solving -25 + 16b2 = 25 + b Solving for variable 'b'. Reorder the terms: -25 + -25 + -1b + 16b2 = 25 + b + -25 + -1b Combine like terms: -25 + -25 = -50 -50 + -1b + 16b2 = 25 + b + -25 + -1b Reorder the terms: -50 + -1b + 16b2 = 25 + -25 + b + -1b Combine like terms: 25 + -25 = 0 -50 + -1b + 16b2 = 0 + b + -1b -50 + -1b + 16b2 = b + -1b Combine like terms: b + -1b = 0 -50 + -1b + 16b2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.125 + -0.0625b + b2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -0.0625b + 3.125 + b2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -0.0625b + b2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -0.0625b + b2 = 0 + 3.125 -0.0625b + b2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -0.0625b + b2 = 3.125 The b term is -0.0625b. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625b + 0.0009765625 + b2 = 3.125 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625b + b2 = 3.125 + 0.0009765625 Combine like terms: 3.125 + 0.0009765625 = 3.1259765625 0.0009765625 + -0.0625b + b2 = 3.1259765625 Factor a perfect square on the left side: (b + -0.03125)(b + -0.03125) = 3.1259765625 Calculate the square root of the right side: 1.768043145 Break this problem into two subproblems by setting (b + -0.03125) equal to 1.768043145 and -1.768043145.Subproblem 1
b + -0.03125 = 1.768043145 Simplifying b + -0.03125 = 1.768043145 Reorder the terms: -0.03125 + b = 1.768043145 Solving -0.03125 + b = 1.768043145 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + b = 1.768043145 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + b = 1.768043145 + 0.03125 b = 1.768043145 + 0.03125 Combine like terms: 1.768043145 + 0.03125 = 1.799293145 b = 1.799293145 Simplifying b = 1.799293145Subproblem 2
b + -0.03125 = -1.768043145 Simplifying b + -0.03125 = -1.768043145 Reorder the terms: -0.03125 + b = -1.768043145 Solving -0.03125 + b = -1.768043145 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + b = -1.768043145 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + b = -1.768043145 + 0.03125 b = -1.768043145 + 0.03125 Combine like terms: -1.768043145 + 0.03125 = -1.736793145 b = -1.736793145 Simplifying b = -1.736793145Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.799293145, -1.736793145}
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