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Simplifying 4b2 = 17 + b Solving 4b2 = 17 + b Solving for variable 'b'. Reorder the terms: -17 + -1b + 4b2 = 17 + b + -17 + -1b Reorder the terms: -17 + -1b + 4b2 = 17 + -17 + b + -1b Combine like terms: 17 + -17 = 0 -17 + -1b + 4b2 = 0 + b + -1b -17 + -1b + 4b2 = b + -1b Combine like terms: b + -1b = 0 -17 + -1b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -0.25b + b2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -0.25b + 4.25 + b2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -0.25b + b2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -0.25b + b2 = 0 + 4.25 -0.25b + b2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -0.25b + b2 = 4.25 The b term is -0.25b. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25b + 0.015625 + b2 = 4.25 + 0.015625 Reorder the terms: 0.015625 + -0.25b + b2 = 4.25 + 0.015625 Combine like terms: 4.25 + 0.015625 = 4.265625 0.015625 + -0.25b + b2 = 4.265625 Factor a perfect square on the left side: (b + -0.125)(b + -0.125) = 4.265625 Calculate the square root of the right side: 2.065338955 Break this problem into two subproblems by setting (b + -0.125) equal to 2.065338955 and -2.065338955.Subproblem 1
b + -0.125 = 2.065338955 Simplifying b + -0.125 = 2.065338955 Reorder the terms: -0.125 + b = 2.065338955 Solving -0.125 + b = 2.065338955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = 2.065338955 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = 2.065338955 + 0.125 b = 2.065338955 + 0.125 Combine like terms: 2.065338955 + 0.125 = 2.190338955 b = 2.190338955 Simplifying b = 2.190338955Subproblem 2
b + -0.125 = -2.065338955 Simplifying b + -0.125 = -2.065338955 Reorder the terms: -0.125 + b = -2.065338955 Solving -0.125 + b = -2.065338955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = -2.065338955 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = -2.065338955 + 0.125 b = -2.065338955 + 0.125 Combine like terms: -2.065338955 + 0.125 = -1.940338955 b = -1.940338955 Simplifying b = -1.940338955Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.190338955, -1.940338955}
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