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Simplifying 9(y + 6) + 2y(y + 3) = 0 Reorder the terms: 9(6 + y) + 2y(y + 3) = 0 (6 * 9 + y * 9) + 2y(y + 3) = 0 (54 + 9y) + 2y(y + 3) = 0 Reorder the terms: 54 + 9y + 2y(3 + y) = 0 54 + 9y + (3 * 2y + y * 2y) = 0 54 + 9y + (6y + 2y2) = 0 Combine like terms: 9y + 6y = 15y 54 + 15y + 2y2 = 0 Solving 54 + 15y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27 + 7.5y + y2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 7.5y + -27 + y2 = 0 + -27 Reorder the terms: 27 + -27 + 7.5y + y2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 7.5y + y2 = 0 + -27 7.5y + y2 = 0 + -27 Combine like terms: 0 + -27 = -27 7.5y + y2 = -27 The y term is 7.5y. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5y + 14.0625 + y2 = -27 + 14.0625 Reorder the terms: 14.0625 + 7.5y + y2 = -27 + 14.0625 Combine like terms: -27 + 14.0625 = -12.9375 14.0625 + 7.5y + y2 = -12.9375 Factor a perfect square on the left side: (y + 3.75)(y + 3.75) = -12.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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