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Simplifying 13y2 + 17y + 12 = 6y2 + 2y + 2 Reorder the terms: 12 + 17y + 13y2 = 6y2 + 2y + 2 Reorder the terms: 12 + 17y + 13y2 = 2 + 2y + 6y2 Solving 12 + 17y + 13y2 = 2 + 2y + 6y2 Solving for variable 'y'. Reorder the terms: 12 + -2 + 17y + -2y + 13y2 + -6y2 = 2 + 2y + 6y2 + -2 + -2y + -6y2 Combine like terms: 12 + -2 = 10 10 + 17y + -2y + 13y2 + -6y2 = 2 + 2y + 6y2 + -2 + -2y + -6y2 Combine like terms: 17y + -2y = 15y 10 + 15y + 13y2 + -6y2 = 2 + 2y + 6y2 + -2 + -2y + -6y2 Combine like terms: 13y2 + -6y2 = 7y2 10 + 15y + 7y2 = 2 + 2y + 6y2 + -2 + -2y + -6y2 Reorder the terms: 10 + 15y + 7y2 = 2 + -2 + 2y + -2y + 6y2 + -6y2 Combine like terms: 2 + -2 = 0 10 + 15y + 7y2 = 0 + 2y + -2y + 6y2 + -6y2 10 + 15y + 7y2 = 2y + -2y + 6y2 + -6y2 Combine like terms: 2y + -2y = 0 10 + 15y + 7y2 = 0 + 6y2 + -6y2 10 + 15y + 7y2 = 6y2 + -6y2 Combine like terms: 6y2 + -6y2 = 0 10 + 15y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.428571429 + 2.142857143y + y2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + 2.142857143y + -1.428571429 + y2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + 2.142857143y + y2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + 2.142857143y + y2 = 0 + -1.428571429 2.142857143y + y2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 2.142857143y + y2 = -1.428571429 The y term is 2.142857143y. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143y + 1.147959185 + y2 = -1.428571429 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143y + y2 = -1.428571429 + 1.147959185 Combine like terms: -1.428571429 + 1.147959185 = -0.280612244 1.147959185 + 2.142857143y + y2 = -0.280612244 Factor a perfect square on the left side: (y + 1.071428572)(y + 1.071428572) = -0.280612244 Can't calculate square root of the right side. The solution to this equation could not be determined.
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