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Simplifying b2 = 8 + 2b + 6 + -5 Reorder the terms: b2 = 8 + 6 + -5 + 2b Combine like terms: 8 + 6 = 14 b2 = 14 + -5 + 2b Combine like terms: 14 + -5 = 9 b2 = 9 + 2b Solving b2 = 9 + 2b Solving for variable 'b'. Reorder the terms: -9 + -2b + b2 = 9 + 2b + -9 + -2b Reorder the terms: -9 + -2b + b2 = 9 + -9 + 2b + -2b Combine like terms: 9 + -9 = 0 -9 + -2b + b2 = 0 + 2b + -2b -9 + -2b + b2 = 2b + -2b Combine like terms: 2b + -2b = 0 -9 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2b + 9 + b2 = 0 + 9 Reorder the terms: -9 + 9 + -2b + b2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2b + b2 = 0 + 9 -2b + b2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2b + b2 = 9 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 9 + 1 Reorder the terms: 1 + -2b + b2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2b + b2 = 10 Factor a perfect square on the left side: (b + -1)(b + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (b + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
b + -1 = 3.16227766 Simplifying b + -1 = 3.16227766 Reorder the terms: -1 + b = 3.16227766 Solving -1 + b = 3.16227766 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + b = 3.16227766 + 1 b = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 b = 4.16227766 Simplifying b = 4.16227766Subproblem 2
b + -1 = -3.16227766 Simplifying b + -1 = -3.16227766 Reorder the terms: -1 + b = -3.16227766 Solving -1 + b = -3.16227766 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + b = -3.16227766 + 1 b = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 b = -2.16227766 Simplifying b = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.16227766, -2.16227766}
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