6y^2-y-11=0

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Solution for 6y^2-y-11=0 equation:


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 = 1.43990171635

Subproblem 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 = -1.27323504965

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.43990171635, -1.27323504965}

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