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Simplifying 6y2 + -1y + -11 = 0 Reorder the terms: -11 + -1y + 6y2 = 0 Solving -11 + -1y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + -0.1666666667y + y2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -0.1666666667y + 1.833333333 + y2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -0.1666666667y + y2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -0.1666666667y + y2 = 0 + 1.833333333 -0.1666666667y + y2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -0.1666666667y + y2 = 1.833333333 The y term is -0.1666666667y. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667y + 0.006944444447 + y2 = 1.833333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667y + y2 = 1.833333333 + 0.006944444447 Combine like terms: 1.833333333 + 0.006944444447 = 1.840277777447 0.006944444447 + -0.1666666667y + y2 = 1.840277777447 Factor a perfect square on the left side: (y + -0.08333333335)(y + -0.08333333335) = 1.840277777447 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (y + -0.08333333335) equal to 1.356568383 and -1.356568383.Subproblem 1
y + -0.08333333335 = 1.356568383 Simplifying y + -0.08333333335 = 1.356568383 Reorder the terms: -0.08333333335 + y = 1.356568383 Solving -0.08333333335 + y = 1.356568383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + y = 1.356568383 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = 1.356568383 + 0.08333333335 y = 1.356568383 + 0.08333333335 Combine like terms: 1.356568383 + 0.08333333335 = 1.43990171635 y = 1.43990171635 Simplifying y = 1.43990171635Subproblem 2
y + -0.08333333335 = -1.356568383 Simplifying y + -0.08333333335 = -1.356568383 Reorder the terms: -0.08333333335 + y = -1.356568383 Solving -0.08333333335 + y = -1.356568383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + y = -1.356568383 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = -1.356568383 + 0.08333333335 y = -1.356568383 + 0.08333333335 Combine like terms: -1.356568383 + 0.08333333335 = -1.27323504965 y = -1.27323504965 Simplifying y = -1.27323504965Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.43990171635, -1.27323504965}
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