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Simplifying (b + 250) + -1b2 = 1275 Reorder the terms: (250 + b) + -1b2 = 1275 Remove parenthesis around (250 + b) 250 + b + -1b2 = 1275 Solving 250 + b + -1b2 = 1275 Solving for variable 'b'. Reorder the terms: 250 + -1275 + b + -1b2 = 1275 + -1275 Combine like terms: 250 + -1275 = -1025 -1025 + b + -1b2 = 1275 + -1275 Combine like terms: 1275 + -1275 = 0 -1025 + b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1025 + -1b + b2 = 0 Move the constant term to the right: Add '-1025' to each side of the equation. 1025 + -1b + -1025 + b2 = 0 + -1025 Reorder the terms: 1025 + -1025 + -1b + b2 = 0 + -1025 Combine like terms: 1025 + -1025 = 0 0 + -1b + b2 = 0 + -1025 -1b + b2 = 0 + -1025 Combine like terms: 0 + -1025 = -1025 -1b + b2 = -1025 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. -1b + 0.25 + b2 = -1025 + 0.25 Reorder the terms: 0.25 + -1b + b2 = -1025 + 0.25 Combine like terms: -1025 + 0.25 = -1024.75 0.25 + -1b + b2 = -1024.75 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = -1024.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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