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Simplifying 3y + 1 = -4y2 Reorder the terms: 1 + 3y = -4y2 Solving 1 + 3y = -4y2 Solving for variable 'y'. Combine like terms: -4y2 + 4y2 = 0 1 + 3y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 0.75y + y2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.75y + -0.25 + y2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.75y + y2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.75y + y2 = 0 + -0.25 0.75y + y2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.75y + y2 = -0.25 The y term is 0.75y. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75y + 0.140625 + y2 = -0.25 + 0.140625 Reorder the terms: 0.140625 + 0.75y + y2 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + 0.75y + y2 = -0.109375 Factor a perfect square on the left side: (y + 0.375)(y + 0.375) = -0.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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