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Simplifying (4y + -7)(y + 11) + -1(5y + 1)(9y + -2) = 17 + -1y Reorder the terms: (-7 + 4y)(y + 11) + -1(5y + 1)(9y + -2) = 17 + -1y Reorder the terms: (-7 + 4y)(11 + y) + -1(5y + 1)(9y + -2) = 17 + -1y Multiply (-7 + 4y) * (11 + y) (-7(11 + y) + 4y * (11 + y)) + -1(5y + 1)(9y + -2) = 17 + -1y ((11 * -7 + y * -7) + 4y * (11 + y)) + -1(5y + 1)(9y + -2) = 17 + -1y ((-77 + -7y) + 4y * (11 + y)) + -1(5y + 1)(9y + -2) = 17 + -1y (-77 + -7y + (11 * 4y + y * 4y)) + -1(5y + 1)(9y + -2) = 17 + -1y (-77 + -7y + (44y + 4y2)) + -1(5y + 1)(9y + -2) = 17 + -1y Combine like terms: -7y + 44y = 37y (-77 + 37y + 4y2) + -1(5y + 1)(9y + -2) = 17 + -1y Reorder the terms: -77 + 37y + 4y2 + -1(1 + 5y)(9y + -2) = 17 + -1y Reorder the terms: -77 + 37y + 4y2 + -1(1 + 5y)(-2 + 9y) = 17 + -1y Multiply (1 + 5y) * (-2 + 9y) -77 + 37y + 4y2 + -1(1(-2 + 9y) + 5y * (-2 + 9y)) = 17 + -1y -77 + 37y + 4y2 + -1((-2 * 1 + 9y * 1) + 5y * (-2 + 9y)) = 17 + -1y -77 + 37y + 4y2 + -1((-2 + 9y) + 5y * (-2 + 9y)) = 17 + -1y -77 + 37y + 4y2 + -1(-2 + 9y + (-2 * 5y + 9y * 5y)) = 17 + -1y -77 + 37y + 4y2 + -1(-2 + 9y + (-10y + 45y2)) = 17 + -1y Combine like terms: 9y + -10y = -1y -77 + 37y + 4y2 + -1(-2 + -1y + 45y2) = 17 + -1y -77 + 37y + 4y2 + (-2 * -1 + -1y * -1 + 45y2 * -1) = 17 + -1y -77 + 37y + 4y2 + (2 + 1y + -45y2) = 17 + -1y Reorder the terms: -77 + 2 + 37y + 1y + 4y2 + -45y2 = 17 + -1y Combine like terms: -77 + 2 = -75 -75 + 37y + 1y + 4y2 + -45y2 = 17 + -1y Combine like terms: 37y + 1y = 38y -75 + 38y + 4y2 + -45y2 = 17 + -1y Combine like terms: 4y2 + -45y2 = -41y2 -75 + 38y + -41y2 = 17 + -1y Solving -75 + 38y + -41y2 = 17 + -1y Solving for variable 'y'. Reorder the terms: -75 + -17 + 38y + y + -41y2 = 17 + -1y + -17 + y Combine like terms: -75 + -17 = -92 -92 + 38y + y + -41y2 = 17 + -1y + -17 + y Combine like terms: 38y + y = 39y -92 + 39y + -41y2 = 17 + -1y + -17 + y Reorder the terms: -92 + 39y + -41y2 = 17 + -17 + -1y + y Combine like terms: 17 + -17 = 0 -92 + 39y + -41y2 = 0 + -1y + y -92 + 39y + -41y2 = -1y + y Combine like terms: -1y + y = 0 -92 + 39y + -41y2 = 0 Begin completing the square. Divide all terms by -41 the coefficient of the squared term: Divide each side by '-41'. 2.243902439 + -0.9512195122y + y2 = 0 Move the constant term to the right: Add '-2.243902439' to each side of the equation. 2.243902439 + -0.9512195122y + -2.243902439 + y2 = 0 + -2.243902439 Reorder the terms: 2.243902439 + -2.243902439 + -0.9512195122y + y2 = 0 + -2.243902439 Combine like terms: 2.243902439 + -2.243902439 = 0.000000000 0.000000000 + -0.9512195122y + y2 = 0 + -2.243902439 -0.9512195122y + y2 = 0 + -2.243902439 Combine like terms: 0 + -2.243902439 = -2.243902439 -0.9512195122y + y2 = -2.243902439 The y term is -0.9512195122y. Take half its coefficient (-0.4756097561). Square it (0.2262046401) and add it to both sides. Add '0.2262046401' to each side of the equation. -0.9512195122y + 0.2262046401 + y2 = -2.243902439 + 0.2262046401 Reorder the terms: 0.2262046401 + -0.9512195122y + y2 = -2.243902439 + 0.2262046401 Combine like terms: -2.243902439 + 0.2262046401 = -2.0176977989 0.2262046401 + -0.9512195122y + y2 = -2.0176977989 Factor a perfect square on the left side: (y + -0.4756097561)(y + -0.4756097561) = -2.0176977989 Can't calculate square root of the right side. The solution to this equation could not be determined.
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