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Simplifying -11y2 + 2y + 7 = 0 Reorder the terms: 7 + 2y + -11y2 = 0 Solving 7 + 2y + -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 + -0.1818181818y + y2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + -0.1818181818y + 0.6363636364 + y2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + -0.1818181818y + y2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + -0.1818181818y + y2 = 0 + 0.6363636364 -0.1818181818y + y2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 -0.1818181818y + y2 = 0.6363636364 The y term is -0.1818181818y. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818y + 0.008264462808 + y2 = 0.6363636364 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818y + y2 = 0.6363636364 + 0.008264462808 Combine like terms: 0.6363636364 + 0.008264462808 = 0.644628099208 0.008264462808 + -0.1818181818y + y2 = 0.644628099208 Factor a perfect square on the left side: (y + -0.0909090909)(y + -0.0909090909) = 0.644628099208 Calculate the square root of the right side: 0.802887352 Break this problem into two subproblems by setting (y + -0.0909090909) equal to 0.802887352 and -0.802887352.Subproblem 1
y + -0.0909090909 = 0.802887352 Simplifying y + -0.0909090909 = 0.802887352 Reorder the terms: -0.0909090909 + y = 0.802887352 Solving -0.0909090909 + y = 0.802887352 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + y = 0.802887352 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + y = 0.802887352 + 0.0909090909 y = 0.802887352 + 0.0909090909 Combine like terms: 0.802887352 + 0.0909090909 = 0.8937964429 y = 0.8937964429 Simplifying y = 0.8937964429Subproblem 2
y + -0.0909090909 = -0.802887352 Simplifying y + -0.0909090909 = -0.802887352 Reorder the terms: -0.0909090909 + y = -0.802887352 Solving -0.0909090909 + y = -0.802887352 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + y = -0.802887352 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + y = -0.802887352 + 0.0909090909 y = -0.802887352 + 0.0909090909 Combine like terms: -0.802887352 + 0.0909090909 = -0.7119782611 y = -0.7119782611 Simplifying y = -0.7119782611Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8937964429, -0.7119782611}
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