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Simplifying (4y + -5)(6 + -7y) + -8(5y + 7) = 0 Reorder the terms: (-5 + 4y)(6 + -7y) + -8(5y + 7) = 0 Multiply (-5 + 4y) * (6 + -7y) (-5(6 + -7y) + 4y * (6 + -7y)) + -8(5y + 7) = 0 ((6 * -5 + -7y * -5) + 4y * (6 + -7y)) + -8(5y + 7) = 0 ((-30 + 35y) + 4y * (6 + -7y)) + -8(5y + 7) = 0 (-30 + 35y + (6 * 4y + -7y * 4y)) + -8(5y + 7) = 0 (-30 + 35y + (24y + -28y2)) + -8(5y + 7) = 0 Combine like terms: 35y + 24y = 59y (-30 + 59y + -28y2) + -8(5y + 7) = 0 Reorder the terms: -30 + 59y + -28y2 + -8(7 + 5y) = 0 -30 + 59y + -28y2 + (7 * -8 + 5y * -8) = 0 -30 + 59y + -28y2 + (-56 + -40y) = 0 Reorder the terms: -30 + -56 + 59y + -40y + -28y2 = 0 Combine like terms: -30 + -56 = -86 -86 + 59y + -40y + -28y2 = 0 Combine like terms: 59y + -40y = 19y -86 + 19y + -28y2 = 0 Solving -86 + 19y + -28y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -28 the coefficient of the squared term: Divide each side by '-28'. 3.071428571 + -0.6785714286y + y2 = 0 Move the constant term to the right: Add '-3.071428571' to each side of the equation. 3.071428571 + -0.6785714286y + -3.071428571 + y2 = 0 + -3.071428571 Reorder the terms: 3.071428571 + -3.071428571 + -0.6785714286y + y2 = 0 + -3.071428571 Combine like terms: 3.071428571 + -3.071428571 = 0.000000000 0.000000000 + -0.6785714286y + y2 = 0 + -3.071428571 -0.6785714286y + y2 = 0 + -3.071428571 Combine like terms: 0 + -3.071428571 = -3.071428571 -0.6785714286y + y2 = -3.071428571 The y term is -0.6785714286y. Take half its coefficient (-0.3392857143). Square it (0.1151147959) and add it to both sides. Add '0.1151147959' to each side of the equation. -0.6785714286y + 0.1151147959 + y2 = -3.071428571 + 0.1151147959 Reorder the terms: 0.1151147959 + -0.6785714286y + y2 = -3.071428571 + 0.1151147959 Combine like terms: -3.071428571 + 0.1151147959 = -2.9563137751 0.1151147959 + -0.6785714286y + y2 = -2.9563137751 Factor a perfect square on the left side: (y + -0.3392857143)(y + -0.3392857143) = -2.9563137751 Can't calculate square root of the right side. The solution to this equation could not be determined.
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