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Simplifying (y + -4) * 2 + -7(2 + -1y) = (y + 5)(y + -2) Reorder the terms: (-4 + y) * 2 + -7(2 + -1y) = (y + 5)(y + -2) Reorder the terms for easier multiplication: 2(-4 + y) + -7(2 + -1y) = (y + 5)(y + -2) (-4 * 2 + y * 2) + -7(2 + -1y) = (y + 5)(y + -2) (-8 + 2y) + -7(2 + -1y) = (y + 5)(y + -2) -8 + 2y + (2 * -7 + -1y * -7) = (y + 5)(y + -2) -8 + 2y + (-14 + 7y) = (y + 5)(y + -2) Reorder the terms: -8 + -14 + 2y + 7y = (y + 5)(y + -2) Combine like terms: -8 + -14 = -22 -22 + 2y + 7y = (y + 5)(y + -2) Combine like terms: 2y + 7y = 9y -22 + 9y = (y + 5)(y + -2) Reorder the terms: -22 + 9y = (5 + y)(y + -2) Reorder the terms: -22 + 9y = (5 + y)(-2 + y) Multiply (5 + y) * (-2 + y) -22 + 9y = (5(-2 + y) + y(-2 + y)) -22 + 9y = ((-2 * 5 + y * 5) + y(-2 + y)) -22 + 9y = ((-10 + 5y) + y(-2 + y)) -22 + 9y = (-10 + 5y + (-2 * y + y * y)) -22 + 9y = (-10 + 5y + (-2y + y2)) Combine like terms: 5y + -2y = 3y -22 + 9y = (-10 + 3y + y2) Solving -22 + 9y = -10 + 3y + y2 Solving for variable 'y'. Reorder the terms: -22 + 10 + 9y + -3y + -1y2 = -10 + 3y + y2 + 10 + -3y + -1y2 Combine like terms: -22 + 10 = -12 -12 + 9y + -3y + -1y2 = -10 + 3y + y2 + 10 + -3y + -1y2 Combine like terms: 9y + -3y = 6y -12 + 6y + -1y2 = -10 + 3y + y2 + 10 + -3y + -1y2 Reorder the terms: -12 + 6y + -1y2 = -10 + 10 + 3y + -3y + y2 + -1y2 Combine like terms: -10 + 10 = 0 -12 + 6y + -1y2 = 0 + 3y + -3y + y2 + -1y2 -12 + 6y + -1y2 = 3y + -3y + y2 + -1y2 Combine like terms: 3y + -3y = 0 -12 + 6y + -1y2 = 0 + y2 + -1y2 -12 + 6y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -12 + 6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -6y + y2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -6y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + -6y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6y + y2 = 0 + -12 -6y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 -6y + y2 = -12 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 = -12 + 9 Reorder the terms: 9 + -6y + y2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + -6y + y2 = -3 Factor a perfect square on the left side: (y + -3)(y + -3) = -3 Can't calculate square root of the right side. The solution to this equation could not be determined.
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