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Simplifying b2 + b + -9 = 0 Reorder the terms: -9 + b + b2 = 0 Solving -9 + b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + b + 9 + b2 = 0 + 9 Reorder the terms: -9 + 9 + b + b2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + b + b2 = 0 + 9 b + b2 = 0 + 9 Combine like terms: 0 + 9 = 9 b + b2 = 9 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 = 9 + 0.25 Reorder the terms: 0.25 + b + b2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + b + b2 = 9.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (b + 0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
b + 0.5 = 3.041381265 Simplifying b + 0.5 = 3.041381265 Reorder the terms: 0.5 + b = 3.041381265 Solving 0.5 + b = 3.041381265 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 = 3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 3.041381265 + -0.5 b = 3.041381265 + -0.5 Combine like terms: 3.041381265 + -0.5 = 2.541381265 b = 2.541381265 Simplifying b = 2.541381265Subproblem 2
b + 0.5 = -3.041381265 Simplifying b + 0.5 = -3.041381265 Reorder the terms: 0.5 + b = -3.041381265 Solving 0.5 + b = -3.041381265 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 = -3.041381265 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -3.041381265 + -0.5 b = -3.041381265 + -0.5 Combine like terms: -3.041381265 + -0.5 = -3.541381265 b = -3.541381265 Simplifying b = -3.541381265Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.541381265, -3.541381265}
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