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Simplifying 2y2 + 5y + 24 = 0 Reorder the terms: 24 + 5y + 2y2 = 0 Solving 24 + 5y + 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'. 12 + 2.5y + y2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 2.5y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + 2.5y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 2.5y + y2 = 0 + -12 2.5y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 2.5y + y2 = -12 The y term is 2.5y. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5y + 1.5625 + y2 = -12 + 1.5625 Reorder the terms: 1.5625 + 2.5y + y2 = -12 + 1.5625 Combine like terms: -12 + 1.5625 = -10.4375 1.5625 + 2.5y + y2 = -10.4375 Factor a perfect square on the left side: (y + 1.25)(y + 1.25) = -10.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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