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Simplifying 6y + 10 = y2 + 34 Reorder the terms: 10 + 6y = y2 + 34 Reorder the terms: 10 + 6y = 34 + y2 Solving 10 + 6y = 34 + y2 Solving for variable 'y'. Reorder the terms: 10 + -34 + 6y + -1y2 = 34 + y2 + -34 + -1y2 Combine like terms: 10 + -34 = -24 -24 + 6y + -1y2 = 34 + y2 + -34 + -1y2 Reorder the terms: -24 + 6y + -1y2 = 34 + -34 + y2 + -1y2 Combine like terms: 34 + -34 = 0 -24 + 6y + -1y2 = 0 + y2 + -1y2 -24 + 6y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -24 + 6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -6y + y2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -6y + -24 + y2 = 0 + -24 Reorder the terms: 24 + -24 + -6y + y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -6y + y2 = 0 + -24 -6y + y2 = 0 + -24 Combine like terms: 0 + -24 = -24 -6y + y2 = -24 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 = -24 + 9 Reorder the terms: 9 + -6y + y2 = -24 + 9 Combine like terms: -24 + 9 = -15 9 + -6y + y2 = -15 Factor a perfect square on the left side: (y + -3)(y + -3) = -15 Can't calculate square root of the right side. The solution to this equation could not be determined.
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