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Simplifying 11y2 + -42y + -141 = 0 Reorder the terms: -141 + -42y + 11y2 = 0 Solving -141 + -42y + 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'. -12.81818182 + -3.818181818y + y2 = 0 Move the constant term to the right: Add '12.81818182' to each side of the equation. -12.81818182 + -3.818181818y + 12.81818182 + y2 = 0 + 12.81818182 Reorder the terms: -12.81818182 + 12.81818182 + -3.818181818y + y2 = 0 + 12.81818182 Combine like terms: -12.81818182 + 12.81818182 = 0.00000000 0.00000000 + -3.818181818y + y2 = 0 + 12.81818182 -3.818181818y + y2 = 0 + 12.81818182 Combine like terms: 0 + 12.81818182 = 12.81818182 -3.818181818y + y2 = 12.81818182 The y term is -3.818181818y. Take half its coefficient (-1.909090909). Square it (3.644628099) and add it to both sides. Add '3.644628099' to each side of the equation. -3.818181818y + 3.644628099 + y2 = 12.81818182 + 3.644628099 Reorder the terms: 3.644628099 + -3.818181818y + y2 = 12.81818182 + 3.644628099 Combine like terms: 12.81818182 + 3.644628099 = 16.462809919 3.644628099 + -3.818181818y + y2 = 16.462809919 Factor a perfect square on the left side: (y + -1.909090909)(y + -1.909090909) = 16.462809919 Calculate the square root of the right side: 4.057438837 Break this problem into two subproblems by setting (y + -1.909090909) equal to 4.057438837 and -4.057438837.Subproblem 1
y + -1.909090909 = 4.057438837 Simplifying y + -1.909090909 = 4.057438837 Reorder the terms: -1.909090909 + y = 4.057438837 Solving -1.909090909 + y = 4.057438837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.909090909' to each side of the equation. -1.909090909 + 1.909090909 + y = 4.057438837 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + y = 4.057438837 + 1.909090909 y = 4.057438837 + 1.909090909 Combine like terms: 4.057438837 + 1.909090909 = 5.966529746 y = 5.966529746 Simplifying y = 5.966529746Subproblem 2
y + -1.909090909 = -4.057438837 Simplifying y + -1.909090909 = -4.057438837 Reorder the terms: -1.909090909 + y = -4.057438837 Solving -1.909090909 + y = -4.057438837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.909090909' to each side of the equation. -1.909090909 + 1.909090909 + y = -4.057438837 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + y = -4.057438837 + 1.909090909 y = -4.057438837 + 1.909090909 Combine like terms: -4.057438837 + 1.909090909 = -2.148347928 y = -2.148347928 Simplifying y = -2.148347928Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.966529746, -2.148347928}
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