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Simplifying 11y2 + -80y + -218 = 0 Reorder the terms: -218 + -80y + 11y2 = 0 Solving -218 + -80y + 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'. -19.81818182 + -7.272727273y + y2 = 0 Move the constant term to the right: Add '19.81818182' to each side of the equation. -19.81818182 + -7.272727273y + 19.81818182 + y2 = 0 + 19.81818182 Reorder the terms: -19.81818182 + 19.81818182 + -7.272727273y + y2 = 0 + 19.81818182 Combine like terms: -19.81818182 + 19.81818182 = 0.00000000 0.00000000 + -7.272727273y + y2 = 0 + 19.81818182 -7.272727273y + y2 = 0 + 19.81818182 Combine like terms: 0 + 19.81818182 = 19.81818182 -7.272727273y + y2 = 19.81818182 The y term is -7.272727273y. Take half its coefficient (-3.636363637). Square it (13.22314050) and add it to both sides. Add '13.22314050' to each side of the equation. -7.272727273y + 13.22314050 + y2 = 19.81818182 + 13.22314050 Reorder the terms: 13.22314050 + -7.272727273y + y2 = 19.81818182 + 13.22314050 Combine like terms: 19.81818182 + 13.22314050 = 33.04132232 13.22314050 + -7.272727273y + y2 = 33.04132232 Factor a perfect square on the left side: (y + -3.636363637)(y + -3.636363637) = 33.04132232 Calculate the square root of the right side: 5.748158168 Break this problem into two subproblems by setting (y + -3.636363637) equal to 5.748158168 and -5.748158168.Subproblem 1
y + -3.636363637 = 5.748158168 Simplifying y + -3.636363637 = 5.748158168 Reorder the terms: -3.636363637 + y = 5.748158168 Solving -3.636363637 + y = 5.748158168 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.636363637' to each side of the equation. -3.636363637 + 3.636363637 + y = 5.748158168 + 3.636363637 Combine like terms: -3.636363637 + 3.636363637 = 0.000000000 0.000000000 + y = 5.748158168 + 3.636363637 y = 5.748158168 + 3.636363637 Combine like terms: 5.748158168 + 3.636363637 = 9.384521805 y = 9.384521805 Simplifying y = 9.384521805Subproblem 2
y + -3.636363637 = -5.748158168 Simplifying y + -3.636363637 = -5.748158168 Reorder the terms: -3.636363637 + y = -5.748158168 Solving -3.636363637 + y = -5.748158168 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.636363637' to each side of the equation. -3.636363637 + 3.636363637 + y = -5.748158168 + 3.636363637 Combine like terms: -3.636363637 + 3.636363637 = 0.000000000 0.000000000 + y = -5.748158168 + 3.636363637 y = -5.748158168 + 3.636363637 Combine like terms: -5.748158168 + 3.636363637 = -2.111794531 y = -2.111794531 Simplifying y = -2.111794531Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.384521805, -2.111794531}
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