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Simplifying (5y2 + -2y + 6) + -1(-5y2 + 8y + -7) + (-4y2 + 3y + -3) = 0 Reorder the terms: (6 + -2y + 5y2) + -1(-5y2 + 8y + -7) + (-4y2 + 3y + -3) = 0 Remove parenthesis around (6 + -2y + 5y2) 6 + -2y + 5y2 + -1(-5y2 + 8y + -7) + (-4y2 + 3y + -3) = 0 Reorder the terms: 6 + -2y + 5y2 + -1(-7 + 8y + -5y2) + (-4y2 + 3y + -3) = 0 6 + -2y + 5y2 + (-7 * -1 + 8y * -1 + -5y2 * -1) + (-4y2 + 3y + -3) = 0 6 + -2y + 5y2 + (7 + -8y + 5y2) + (-4y2 + 3y + -3) = 0 Reorder the terms: 6 + -2y + 5y2 + 7 + -8y + 5y2 + (-3 + 3y + -4y2) = 0 Remove parenthesis around (-3 + 3y + -4y2) 6 + -2y + 5y2 + 7 + -8y + 5y2 + -3 + 3y + -4y2 = 0 Reorder the terms: 6 + 7 + -3 + -2y + -8y + 3y + 5y2 + 5y2 + -4y2 = 0 Combine like terms: 6 + 7 = 13 13 + -3 + -2y + -8y + 3y + 5y2 + 5y2 + -4y2 = 0 Combine like terms: 13 + -3 = 10 10 + -2y + -8y + 3y + 5y2 + 5y2 + -4y2 = 0 Combine like terms: -2y + -8y = -10y 10 + -10y + 3y + 5y2 + 5y2 + -4y2 = 0 Combine like terms: -10y + 3y = -7y 10 + -7y + 5y2 + 5y2 + -4y2 = 0 Combine like terms: 5y2 + 5y2 = 10y2 10 + -7y + 10y2 + -4y2 = 0 Combine like terms: 10y2 + -4y2 = 6y2 10 + -7y + 6y2 = 0 Solving 10 + -7y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.666666667 + -1.166666667y + y2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.166666667y + -1.666666667 + y2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.166666667y + y2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.166666667y + y2 = 0 + -1.666666667 -1.166666667y + y2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.166666667y + y2 = -1.666666667 The y term is -1.166666667y. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667y + 0.3402777780 + y2 = -1.666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667y + y2 = -1.666666667 + 0.3402777780 Combine like terms: -1.666666667 + 0.3402777780 = -1.326388889 0.3402777780 + -1.166666667y + y2 = -1.326388889 Factor a perfect square on the left side: (y + -0.5833333335)(y + -0.5833333335) = -1.326388889 Can't calculate square root of the right side. The solution to this equation could not be determined.
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