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Simplifying 0 = y2 + -6y + 77 Reorder the terms: 0 = 77 + -6y + y2 Solving 0 = 77 + -6y + y2 Solving for variable 'y'. Combine like terms: 0 + -77 = -77 -77 + 6y + -1y2 = 77 + -6y + y2 + -77 + 6y + -1y2 Reorder the terms: -77 + 6y + -1y2 = 77 + -77 + -6y + 6y + y2 + -1y2 Combine like terms: 77 + -77 = 0 -77 + 6y + -1y2 = 0 + -6y + 6y + y2 + -1y2 -77 + 6y + -1y2 = -6y + 6y + y2 + -1y2 Combine like terms: -6y + 6y = 0 -77 + 6y + -1y2 = 0 + y2 + -1y2 -77 + 6y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -77 + 6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 77 + -6y + y2 = 0 Move the constant term to the right: Add '-77' to each side of the equation. 77 + -6y + -77 + y2 = 0 + -77 Reorder the terms: 77 + -77 + -6y + y2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + -6y + y2 = 0 + -77 -6y + y2 = 0 + -77 Combine like terms: 0 + -77 = -77 -6y + y2 = -77 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -77 + 9 Reorder the terms: 9 + -6y + y2 = -77 + 9 Combine like terms: -77 + 9 = -68 9 + -6y + y2 = -68 Factor a perfect square on the left side: (y + -3)(y + -3) = -68 Can't calculate square root of the right side. The solution to this equation could not be determined.
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