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Simplifying 5b(-1b + 3) = 21 Reorder the terms: 5b(3 + -1b) = 21 (3 * 5b + -1b * 5b) = 21 (15b + -5b2) = 21 Solving 15b + -5b2 = 21 Solving for variable 'b'. Reorder the terms: -21 + 15b + -5b2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 15b + -5b2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 4.2 + -3b + b2 = 0 Move the constant term to the right: Add '-4.2' to each side of the equation. 4.2 + -3b + -4.2 + b2 = 0 + -4.2 Reorder the terms: 4.2 + -4.2 + -3b + b2 = 0 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + -3b + b2 = 0 + -4.2 -3b + b2 = 0 + -4.2 Combine like terms: 0 + -4.2 = -4.2 -3b + b2 = -4.2 The b term is -3b. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3b + 2.25 + b2 = -4.2 + 2.25 Reorder the terms: 2.25 + -3b + b2 = -4.2 + 2.25 Combine like terms: -4.2 + 2.25 = -1.95 2.25 + -3b + b2 = -1.95 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = -1.95 Can't calculate square root of the right side. The solution to this equation could not be determined.
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