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Simplifying 3y(3y + 4) = 4 Reorder the terms: 3y(4 + 3y) = 4 (4 * 3y + 3y * 3y) = 4 (12y + 9y2) = 4 Solving 12y + 9y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + 12y + 9y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 12y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 1.333333333y + y2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 1.333333333y + 0.4444444444 + y2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 1.333333333y + y2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 1.333333333y + y2 = 0 + 0.4444444444 1.333333333y + y2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 1.333333333y + y2 = 0.4444444444 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 = 0.4444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y + y2 = 0.4444444444 + 0.4444444442 Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886 0.4444444442 + 1.333333333y + y2 = 0.8888888886 Factor a perfect square on the left side: (y + 0.6666666665)(y + 0.6666666665) = 0.8888888886 Calculate the square root of the right side: 0.942809041 Break this problem into two subproblems by setting (y + 0.6666666665) equal to 0.942809041 and -0.942809041.Subproblem 1
y + 0.6666666665 = 0.942809041 Simplifying y + 0.6666666665 = 0.942809041 Reorder the terms: 0.6666666665 + y = 0.942809041 Solving 0.6666666665 + y = 0.942809041 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 = 0.942809041 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = 0.942809041 + -0.6666666665 y = 0.942809041 + -0.6666666665 Combine like terms: 0.942809041 + -0.6666666665 = 0.2761423745 y = 0.2761423745 Simplifying y = 0.2761423745Subproblem 2
y + 0.6666666665 = -0.942809041 Simplifying y + 0.6666666665 = -0.942809041 Reorder the terms: 0.6666666665 + y = -0.942809041 Solving 0.6666666665 + y = -0.942809041 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 = -0.942809041 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + y = -0.942809041 + -0.6666666665 y = -0.942809041 + -0.6666666665 Combine like terms: -0.942809041 + -0.6666666665 = -1.6094757075 y = -1.6094757075 Simplifying y = -1.6094757075Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.2761423745, -1.6094757075}
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