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Simplifying (9y2) + -3y + -4 = 0 Reorder the terms: -4 + -3y + (9y2) = 0 Solving -4 + -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'. -0.4444444444 + -0.3333333333y + y2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.3333333333y + 0.4444444444 + y2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.3333333333y + y2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.3333333333y + y2 = 0 + 0.4444444444 -0.3333333333y + y2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.3333333333y + y2 = 0.4444444444 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 = 0.4444444444 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333y + y2 = 0.4444444444 + 0.02777777779 Combine like terms: 0.4444444444 + 0.02777777779 = 0.47222222219 0.02777777779 + -0.3333333333y + y2 = 0.47222222219 Factor a perfect square on the left side: ((y) + -0.1666666667)((y) + -0.1666666667) = 0.47222222219 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting ((y) + -0.1666666667) equal to 0.687184271 and -0.687184271.Subproblem 1
(y) + -0.1666666667 = 0.687184271 Simplifying (y) + -0.1666666667 = 0.687184271 y + -0.1666666667 = 0.687184271 Reorder the terms: -0.1666666667 + y = 0.687184271 Solving -0.1666666667 + y = 0.687184271 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 = 0.687184271 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + y = 0.687184271 + 0.1666666667 y = 0.687184271 + 0.1666666667 Combine like terms: 0.687184271 + 0.1666666667 = 0.8538509377 y = 0.8538509377 Simplifying y = 0.8538509377Subproblem 2
(y) + -0.1666666667 = -0.687184271 Simplifying (y) + -0.1666666667 = -0.687184271 y + -0.1666666667 = -0.687184271 Reorder the terms: -0.1666666667 + y = -0.687184271 Solving -0.1666666667 + y = -0.687184271 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 = -0.687184271 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + y = -0.687184271 + 0.1666666667 y = -0.687184271 + 0.1666666667 Combine like terms: -0.687184271 + 0.1666666667 = -0.5205176043 y = -0.5205176043 Simplifying y = -0.5205176043Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8538509377, -0.5205176043}
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