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Simplifying b2 + b = 8 Reorder the terms: b + b2 = 8 Solving b + b2 = 8 Solving for variable 'b'. Reorder the terms: -8 + b + b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + b + 8 + b2 = 0 + 8 Reorder the terms: -8 + 8 + b + b2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + b + b2 = 0 + 8 b + b2 = 0 + 8 Combine like terms: 0 + 8 = 8 b + b2 = 8 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. b + 0.25 + b2 = 8 + 0.25 Reorder the terms: 0.25 + b + b2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 0.25 + b + b2 = 8.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (b + 0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
b + 0.5 = 2.872281323 Simplifying b + 0.5 = 2.872281323 Reorder the terms: 0.5 + b = 2.872281323 Solving 0.5 + b = 2.872281323 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 2.872281323 + -0.5 b = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 b = 2.372281323 Simplifying b = 2.372281323Subproblem 2
b + 0.5 = -2.872281323 Simplifying b + 0.5 = -2.872281323 Reorder the terms: 0.5 + b = -2.872281323 Solving 0.5 + b = -2.872281323 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -2.872281323 + -0.5 b = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 b = -3.372281323 Simplifying b = -3.372281323Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.372281323, -3.372281323}
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