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Simplifying 9y2 + -12y + -1 = 0 Reorder the terms: -1 + -12y + 9y2 = 0 Solving -1 + -12y + 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'. -0.1111111111 + -1.333333333y + y2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -1.333333333y + 0.1111111111 + y2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -1.333333333y + y2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -1.333333333y + y2 = 0 + 0.1111111111 -1.333333333y + y2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -1.333333333y + y2 = 0.1111111111 The y term is -1.333333333y. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333y + 0.4444444442 + y2 = 0.1111111111 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333y + y2 = 0.1111111111 + 0.4444444442 Combine like terms: 0.1111111111 + 0.4444444442 = 0.5555555553 0.4444444442 + -1.333333333y + y2 = 0.5555555553 Factor a perfect square on the left side: (y + -0.6666666665)(y + -0.6666666665) = 0.5555555553 Calculate the square root of the right side: 0.745355992 Break this problem into two subproblems by setting (y + -0.6666666665) equal to 0.745355992 and -0.745355992.Subproblem 1
y + -0.6666666665 = 0.745355992 Simplifying y + -0.6666666665 = 0.745355992 Reorder the terms: -0.6666666665 + y = 0.745355992 Solving -0.6666666665 + y = 0.745355992 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + y = 0.745355992 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = 0.745355992 + 0.6666666665 y = 0.745355992 + 0.6666666665 Combine like terms: 0.745355992 + 0.6666666665 = 1.4120226585 y = 1.4120226585 Simplifying y = 1.4120226585Subproblem 2
y + -0.6666666665 = -0.745355992 Simplifying y + -0.6666666665 = -0.745355992 Reorder the terms: -0.6666666665 + y = -0.745355992 Solving -0.6666666665 + y = -0.745355992 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + y = -0.745355992 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = -0.745355992 + 0.6666666665 y = -0.745355992 + 0.6666666665 Combine like terms: -0.745355992 + 0.6666666665 = -0.0786893255 y = -0.0786893255 Simplifying y = -0.0786893255Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.4120226585, -0.0786893255}
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