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Simplifying 9y2 + -3y + -8 = 0 Reorder the terms: -8 + -3y + 9y2 = 0 Solving -8 + -3y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -0.3333333333y + y2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.3333333333y + 0.8888888889 + y2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.3333333333y + y2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.3333333333y + y2 = 0 + 0.8888888889 -0.3333333333y + y2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.3333333333y + y2 = 0.8888888889 The y term is -0.3333333333y. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333y + 0.02777777779 + y2 = 0.8888888889 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333y + y2 = 0.8888888889 + 0.02777777779 Combine like terms: 0.8888888889 + 0.02777777779 = 0.91666666669 0.02777777779 + -0.3333333333y + y2 = 0.91666666669 Factor a perfect square on the left side: (y + -0.1666666667)(y + -0.1666666667) = 0.91666666669 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (y + -0.1666666667) equal to 0.957427108 and -0.957427108.Subproblem 1
y + -0.1666666667 = 0.957427108 Simplifying y + -0.1666666667 = 0.957427108 Reorder the terms: -0.1666666667 + y = 0.957427108 Solving -0.1666666667 + y = 0.957427108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + y = 0.957427108 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + y = 0.957427108 + 0.1666666667 y = 0.957427108 + 0.1666666667 Combine like terms: 0.957427108 + 0.1666666667 = 1.1240937747 y = 1.1240937747 Simplifying y = 1.1240937747Subproblem 2
y + -0.1666666667 = -0.957427108 Simplifying y + -0.1666666667 = -0.957427108 Reorder the terms: -0.1666666667 + y = -0.957427108 Solving -0.1666666667 + y = -0.957427108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + y = -0.957427108 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + y = -0.957427108 + 0.1666666667 y = -0.957427108 + 0.1666666667 Combine like terms: -0.957427108 + 0.1666666667 = -0.7907604413 y = -0.7907604413 Simplifying y = -0.7907604413Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.1240937747, -0.7907604413}
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