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Simplifying 121y2 + 66y + 3 = 0 Reorder the terms: 3 + 66y + 121y2 = 0 Solving 3 + 66y + 121y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. 0.02479338843 + 0.5454545455y + y2 = 0 Move the constant term to the right: Add '-0.02479338843' to each side of the equation. 0.02479338843 + 0.5454545455y + -0.02479338843 + y2 = 0 + -0.02479338843 Reorder the terms: 0.02479338843 + -0.02479338843 + 0.5454545455y + y2 = 0 + -0.02479338843 Combine like terms: 0.02479338843 + -0.02479338843 = 0.00000000000 0.00000000000 + 0.5454545455y + y2 = 0 + -0.02479338843 0.5454545455y + y2 = 0 + -0.02479338843 Combine like terms: 0 + -0.02479338843 = -0.02479338843 0.5454545455y + y2 = -0.02479338843 The y term is 0.5454545455y. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455y + 0.07438016533 + y2 = -0.02479338843 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455y + y2 = -0.02479338843 + 0.07438016533 Combine like terms: -0.02479338843 + 0.07438016533 = 0.0495867769 0.07438016533 + 0.5454545455y + y2 = 0.0495867769 Factor a perfect square on the left side: (y + 0.2727272728)(y + 0.2727272728) = 0.0495867769 Calculate the square root of the right side: 0.222680886 Break this problem into two subproblems by setting (y + 0.2727272728) equal to 0.222680886 and -0.222680886.Subproblem 1
y + 0.2727272728 = 0.222680886 Simplifying y + 0.2727272728 = 0.222680886 Reorder the terms: 0.2727272728 + y = 0.222680886 Solving 0.2727272728 + y = 0.222680886 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + y = 0.222680886 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + y = 0.222680886 + -0.2727272728 y = 0.222680886 + -0.2727272728 Combine like terms: 0.222680886 + -0.2727272728 = -0.0500463868 y = -0.0500463868 Simplifying y = -0.0500463868Subproblem 2
y + 0.2727272728 = -0.222680886 Simplifying y + 0.2727272728 = -0.222680886 Reorder the terms: 0.2727272728 + y = -0.222680886 Solving 0.2727272728 + y = -0.222680886 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + y = -0.222680886 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + y = -0.222680886 + -0.2727272728 y = -0.222680886 + -0.2727272728 Combine like terms: -0.222680886 + -0.2727272728 = -0.4954081588 y = -0.4954081588 Simplifying y = -0.4954081588Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.0500463868, -0.4954081588}
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