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Simplifying 11y2 + -20y + 7 = 0 Reorder the terms: 7 + -20y + 11y2 = 0 Solving 7 + -20y + 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'. 0.6363636364 + -1.818181818y + y2 = 0 Move the constant term to the right: Add '-0.6363636364' to each side of the equation. 0.6363636364 + -1.818181818y + -0.6363636364 + y2 = 0 + -0.6363636364 Reorder the terms: 0.6363636364 + -0.6363636364 + -1.818181818y + y2 = 0 + -0.6363636364 Combine like terms: 0.6363636364 + -0.6363636364 = 0.0000000000 0.0000000000 + -1.818181818y + y2 = 0 + -0.6363636364 -1.818181818y + y2 = 0 + -0.6363636364 Combine like terms: 0 + -0.6363636364 = -0.6363636364 -1.818181818y + y2 = -0.6363636364 The y term is -1.818181818y. Take half its coefficient (-0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. -1.818181818y + 0.8264462808 + y2 = -0.6363636364 + 0.8264462808 Reorder the terms: 0.8264462808 + -1.818181818y + y2 = -0.6363636364 + 0.8264462808 Combine like terms: -0.6363636364 + 0.8264462808 = 0.1900826444 0.8264462808 + -1.818181818y + y2 = 0.1900826444 Factor a perfect square on the left side: (y + -0.909090909)(y + -0.909090909) = 0.1900826444 Calculate the square root of the right side: 0.435984684 Break this problem into two subproblems by setting (y + -0.909090909) equal to 0.435984684 and -0.435984684.Subproblem 1
y + -0.909090909 = 0.435984684 Simplifying y + -0.909090909 = 0.435984684 Reorder the terms: -0.909090909 + y = 0.435984684 Solving -0.909090909 + y = 0.435984684 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + y = 0.435984684 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + y = 0.435984684 + 0.909090909 y = 0.435984684 + 0.909090909 Combine like terms: 0.435984684 + 0.909090909 = 1.345075593 y = 1.345075593 Simplifying y = 1.345075593Subproblem 2
y + -0.909090909 = -0.435984684 Simplifying y + -0.909090909 = -0.435984684 Reorder the terms: -0.909090909 + y = -0.435984684 Solving -0.909090909 + y = -0.435984684 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + y = -0.435984684 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + y = -0.435984684 + 0.909090909 y = -0.435984684 + 0.909090909 Combine like terms: -0.435984684 + 0.909090909 = 0.473106225 y = 0.473106225 Simplifying y = 0.473106225Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.345075593, 0.473106225}
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