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Simplifying 11y2 + -12y + 2 = 0 Reorder the terms: 2 + -12y + 11y2 = 0 Solving 2 + -12y + 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'. 0.1818181818 + -1.090909091y + y2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + -1.090909091y + -0.1818181818 + y2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + -1.090909091y + y2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + -1.090909091y + y2 = 0 + -0.1818181818 -1.090909091y + y2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 -1.090909091y + y2 = -0.1818181818 The y term is -1.090909091y. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091y + 0.2975206612 + y2 = -0.1818181818 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091y + y2 = -0.1818181818 + 0.2975206612 Combine like terms: -0.1818181818 + 0.2975206612 = 0.1157024794 0.2975206612 + -1.090909091y + y2 = 0.1157024794 Factor a perfect square on the left side: (y + -0.5454545455)(y + -0.5454545455) = 0.1157024794 Calculate the square root of the right side: 0.340150672 Break this problem into two subproblems by setting (y + -0.5454545455) equal to 0.340150672 and -0.340150672.Subproblem 1
y + -0.5454545455 = 0.340150672 Simplifying y + -0.5454545455 = 0.340150672 Reorder the terms: -0.5454545455 + y = 0.340150672 Solving -0.5454545455 + y = 0.340150672 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + y = 0.340150672 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = 0.340150672 + 0.5454545455 y = 0.340150672 + 0.5454545455 Combine like terms: 0.340150672 + 0.5454545455 = 0.8856052175 y = 0.8856052175 Simplifying y = 0.8856052175Subproblem 2
y + -0.5454545455 = -0.340150672 Simplifying y + -0.5454545455 = -0.340150672 Reorder the terms: -0.5454545455 + y = -0.340150672 Solving -0.5454545455 + y = -0.340150672 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + y = -0.340150672 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + y = -0.340150672 + 0.5454545455 y = -0.340150672 + 0.5454545455 Combine like terms: -0.340150672 + 0.5454545455 = 0.2053038735 y = 0.2053038735 Simplifying y = 0.2053038735Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8856052175, 0.2053038735}
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