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Simplifying b2 + 10b + 25 = 8 Reorder the terms: 25 + 10b + b2 = 8 Solving 25 + 10b + b2 = 8 Solving for variable 'b'. Reorder the terms: 25 + -8 + 10b + b2 = 8 + -8 Combine like terms: 25 + -8 = 17 17 + 10b + b2 = 8 + -8 Combine like terms: 8 + -8 = 0 17 + 10b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 10b + -17 + b2 = 0 + -17 Reorder the terms: 17 + -17 + 10b + b2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 10b + b2 = 0 + -17 10b + b2 = 0 + -17 Combine like terms: 0 + -17 = -17 10b + b2 = -17 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = -17 + 25 Reorder the terms: 25 + 10b + b2 = -17 + 25 Combine like terms: -17 + 25 = 8 25 + 10b + b2 = 8 Factor a perfect square on the left side: (b + 5)(b + 5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (b + 5) equal to 2.828427125 and -2.828427125.Subproblem 1
b + 5 = 2.828427125 Simplifying b + 5 = 2.828427125 Reorder the terms: 5 + b = 2.828427125 Solving 5 + b = 2.828427125 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 2.828427125 + -5 Combine like terms: 5 + -5 = 0 0 + b = 2.828427125 + -5 b = 2.828427125 + -5 Combine like terms: 2.828427125 + -5 = -2.171572875 b = -2.171572875 Simplifying b = -2.171572875Subproblem 2
b + 5 = -2.828427125 Simplifying b + 5 = -2.828427125 Reorder the terms: 5 + b = -2.828427125 Solving 5 + b = -2.828427125 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -2.828427125 + -5 Combine like terms: 5 + -5 = 0 0 + b = -2.828427125 + -5 b = -2.828427125 + -5 Combine like terms: -2.828427125 + -5 = -7.828427125 b = -7.828427125 Simplifying b = -7.828427125Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.171572875, -7.828427125}
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