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Simplifying b + -1(1 + -2b)(b + -3) = -4 Reorder the terms: b + -1(1 + -2b)(-3 + b) = -4 Multiply (1 + -2b) * (-3 + b) b + -1(1(-3 + b) + -2b * (-3 + b)) = -4 b + -1((-3 * 1 + b * 1) + -2b * (-3 + b)) = -4 b + -1((-3 + 1b) + -2b * (-3 + b)) = -4 b + -1(-3 + 1b + (-3 * -2b + b * -2b)) = -4 b + -1(-3 + 1b + (6b + -2b2)) = -4 Combine like terms: 1b + 6b = 7b b + -1(-3 + 7b + -2b2) = -4 b + (-3 * -1 + 7b * -1 + -2b2 * -1) = -4 b + (3 + -7b + 2b2) = -4 Reorder the terms: 3 + b + -7b + 2b2 = -4 Combine like terms: b + -7b = -6b 3 + -6b + 2b2 = -4 Solving 3 + -6b + 2b2 = -4 Solving for variable 'b'. Reorder the terms: 3 + 4 + -6b + 2b2 = -4 + 4 Combine like terms: 3 + 4 = 7 7 + -6b + 2b2 = -4 + 4 Combine like terms: -4 + 4 = 0 7 + -6b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -3b + b2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -3b + -3.5 + b2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -3b + b2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -3b + b2 = 0 + -3.5 -3b + b2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -3b + b2 = -3.5 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 = -3.5 + 2.25 Reorder the terms: 2.25 + -3b + b2 = -3.5 + 2.25 Combine like terms: -3.5 + 2.25 = -1.25 2.25 + -3b + b2 = -1.25 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = -1.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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