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Simplifying 11y2 + -18y + 5 = 0 Reorder the terms: 5 + -18y + 11y2 = 0 Solving 5 + -18y + 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'. 0.4545454545 + -1.636363636y + y2 = 0 Move the constant term to the right: Add '-0.4545454545' to each side of the equation. 0.4545454545 + -1.636363636y + -0.4545454545 + y2 = 0 + -0.4545454545 Reorder the terms: 0.4545454545 + -0.4545454545 + -1.636363636y + y2 = 0 + -0.4545454545 Combine like terms: 0.4545454545 + -0.4545454545 = 0.0000000000 0.0000000000 + -1.636363636y + y2 = 0 + -0.4545454545 -1.636363636y + y2 = 0 + -0.4545454545 Combine like terms: 0 + -0.4545454545 = -0.4545454545 -1.636363636y + y2 = -0.4545454545 The y term is -1.636363636y. Take half its coefficient (-0.818181818). Square it (0.6694214873) and add it to both sides. Add '0.6694214873' to each side of the equation. -1.636363636y + 0.6694214873 + y2 = -0.4545454545 + 0.6694214873 Reorder the terms: 0.6694214873 + -1.636363636y + y2 = -0.4545454545 + 0.6694214873 Combine like terms: -0.4545454545 + 0.6694214873 = 0.2148760328 0.6694214873 + -1.636363636y + y2 = 0.2148760328 Factor a perfect square on the left side: (y + -0.818181818)(y + -0.818181818) = 0.2148760328 Calculate the square root of the right side: 0.463547228 Break this problem into two subproblems by setting (y + -0.818181818) equal to 0.463547228 and -0.463547228.Subproblem 1
y + -0.818181818 = 0.463547228 Simplifying y + -0.818181818 = 0.463547228 Reorder the terms: -0.818181818 + y = 0.463547228 Solving -0.818181818 + y = 0.463547228 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.818181818' to each side of the equation. -0.818181818 + 0.818181818 + y = 0.463547228 + 0.818181818 Combine like terms: -0.818181818 + 0.818181818 = 0.000000000 0.000000000 + y = 0.463547228 + 0.818181818 y = 0.463547228 + 0.818181818 Combine like terms: 0.463547228 + 0.818181818 = 1.281729046 y = 1.281729046 Simplifying y = 1.281729046Subproblem 2
y + -0.818181818 = -0.463547228 Simplifying y + -0.818181818 = -0.463547228 Reorder the terms: -0.818181818 + y = -0.463547228 Solving -0.818181818 + y = -0.463547228 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.818181818' to each side of the equation. -0.818181818 + 0.818181818 + y = -0.463547228 + 0.818181818 Combine like terms: -0.818181818 + 0.818181818 = 0.000000000 0.000000000 + y = -0.463547228 + 0.818181818 y = -0.463547228 + 0.818181818 Combine like terms: -0.463547228 + 0.818181818 = 0.35463459 y = 0.35463459 Simplifying y = 0.35463459Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.281729046, 0.35463459}
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