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Simplifying 4y = y2 + y + 7 Reorder the terms: 4y = 7 + y + y2 Solving 4y = 7 + y + y2 Solving for variable 'y'. Reorder the terms: -7 + 4y + -1y + -1y2 = 7 + y + y2 + -7 + -1y + -1y2 Combine like terms: 4y + -1y = 3y -7 + 3y + -1y2 = 7 + y + y2 + -7 + -1y + -1y2 Reorder the terms: -7 + 3y + -1y2 = 7 + -7 + y + -1y + y2 + -1y2 Combine like terms: 7 + -7 = 0 -7 + 3y + -1y2 = 0 + y + -1y + y2 + -1y2 -7 + 3y + -1y2 = y + -1y + y2 + -1y2 Combine like terms: y + -1y = 0 -7 + 3y + -1y2 = 0 + y2 + -1y2 -7 + 3y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -7 + 3y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -3y + y2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -3y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + -3y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3y + y2 = 0 + -7 -3y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 -3y + y2 = -7 The y term is -3y. 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. -3y + 2.25 + y2 = -7 + 2.25 Reorder the terms: 2.25 + -3y + y2 = -7 + 2.25 Combine like terms: -7 + 2.25 = -4.75 2.25 + -3y + y2 = -4.75 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = -4.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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