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Simplifying 11y2 + -52y + 46 = 0 Reorder the terms: 46 + -52y + 11y2 = 0 Solving 46 + -52y + 11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 4.181818182 + -4.727272727y + y2 = 0 Move the constant term to the right: Add '-4.181818182' to each side of the equation. 4.181818182 + -4.727272727y + -4.181818182 + y2 = 0 + -4.181818182 Reorder the terms: 4.181818182 + -4.181818182 + -4.727272727y + y2 = 0 + -4.181818182 Combine like terms: 4.181818182 + -4.181818182 = 0.000000000 0.000000000 + -4.727272727y + y2 = 0 + -4.181818182 -4.727272727y + y2 = 0 + -4.181818182 Combine like terms: 0 + -4.181818182 = -4.181818182 -4.727272727y + y2 = -4.181818182 The y term is -4.727272727y. Take half its coefficient (-2.363636364). Square it (5.586776861) and add it to both sides. Add '5.586776861' to each side of the equation. -4.727272727y + 5.586776861 + y2 = -4.181818182 + 5.586776861 Reorder the terms: 5.586776861 + -4.727272727y + y2 = -4.181818182 + 5.586776861 Combine like terms: -4.181818182 + 5.586776861 = 1.404958679 5.586776861 + -4.727272727y + y2 = 1.404958679 Factor a perfect square on the left side: (y + -2.363636364)(y + -2.363636364) = 1.404958679 Calculate the square root of the right side: 1.185309529 Break this problem into two subproblems by setting (y + -2.363636364) equal to 1.185309529 and -1.185309529.Subproblem 1
y + -2.363636364 = 1.185309529 Simplifying y + -2.363636364 = 1.185309529 Reorder the terms: -2.363636364 + y = 1.185309529 Solving -2.363636364 + y = 1.185309529 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.363636364' to each side of the equation. -2.363636364 + 2.363636364 + y = 1.185309529 + 2.363636364 Combine like terms: -2.363636364 + 2.363636364 = 0.000000000 0.000000000 + y = 1.185309529 + 2.363636364 y = 1.185309529 + 2.363636364 Combine like terms: 1.185309529 + 2.363636364 = 3.548945893 y = 3.548945893 Simplifying y = 3.548945893Subproblem 2
y + -2.363636364 = -1.185309529 Simplifying y + -2.363636364 = -1.185309529 Reorder the terms: -2.363636364 + y = -1.185309529 Solving -2.363636364 + y = -1.185309529 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.363636364' to each side of the equation. -2.363636364 + 2.363636364 + y = -1.185309529 + 2.363636364 Combine like terms: -2.363636364 + 2.363636364 = 0.000000000 0.000000000 + y = -1.185309529 + 2.363636364 y = -1.185309529 + 2.363636364 Combine like terms: -1.185309529 + 2.363636364 = 1.178326835 y = 1.178326835 Simplifying y = 1.178326835Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.548945893, 1.178326835}
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