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Simplifying 9y2 + -12y + 2 = 0 Reorder the terms: 2 + -12y + 9y2 = 0 Solving 2 + -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'. 0.2222222222 + -1.333333333y + y2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -1.333333333y + -0.2222222222 + y2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -1.333333333y + y2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -1.333333333y + y2 = 0 + -0.2222222222 -1.333333333y + y2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -1.333333333y + y2 = -0.2222222222 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 = -0.2222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333y + y2 = -0.2222222222 + 0.4444444442 Combine like terms: -0.2222222222 + 0.4444444442 = 0.222222222 0.4444444442 + -1.333333333y + y2 = 0.222222222 Factor a perfect square on the left side: (y + -0.6666666665)(y + -0.6666666665) = 0.222222222 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (y + -0.6666666665) equal to 0.471404521 and -0.471404521.Subproblem 1
y + -0.6666666665 = 0.471404521 Simplifying y + -0.6666666665 = 0.471404521 Reorder the terms: -0.6666666665 + y = 0.471404521 Solving -0.6666666665 + y = 0.471404521 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 = 0.471404521 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = 0.471404521 + 0.6666666665 y = 0.471404521 + 0.6666666665 Combine like terms: 0.471404521 + 0.6666666665 = 1.1380711875 y = 1.1380711875 Simplifying y = 1.1380711875Subproblem 2
y + -0.6666666665 = -0.471404521 Simplifying y + -0.6666666665 = -0.471404521 Reorder the terms: -0.6666666665 + y = -0.471404521 Solving -0.6666666665 + y = -0.471404521 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 = -0.471404521 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + y = -0.471404521 + 0.6666666665 y = -0.471404521 + 0.6666666665 Combine like terms: -0.471404521 + 0.6666666665 = 0.1952621455 y = 0.1952621455 Simplifying y = 0.1952621455Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.1380711875, 0.1952621455}
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