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Simplifying 2b(b + 1) = -9 Reorder the terms: 2b(1 + b) = -9 (1 * 2b + b * 2b) = -9 (2b + 2b2) = -9 Solving 2b + 2b2 = -9 Solving for variable 'b'. Reorder the terms: 9 + 2b + 2b2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 2b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + b + b2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + b + -4.5 + b2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + b + b2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + b + b2 = 0 + -4.5 b + b2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 b + b2 = -4.5 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. + 0.25 + b2 = -4.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + b2 = -4.5 + 0.25 Combine like terms: -4.5 + 0.25 = -4.25 1.25 + b2 = -4.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = -4.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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