36y^2+8y-1=0

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Solution for 36y^2+8y-1=0 equation: 


Simplifying
36y2 + 8y + -1 = 0

Reorder the terms:
-1 + 8y + 36y2 = 0

Solving
-1 + 8y + 36y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
36 the coefficient of the squared term: 

Divide each side by '36'.
-0.02777777778 + 0.2222222222y + y2 = 0

Move the constant term to the right:

Add '0.02777777778' to each side of the equation.
-0.02777777778 + 0.2222222222y + 0.02777777778 + y2 = 0 + 0.02777777778

Reorder the terms:
-0.02777777778 + 0.02777777778 + 0.2222222222y + y2 = 0 + 0.02777777778

Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000
0.00000000000 + 0.2222222222y + y2 = 0 + 0.02777777778
0.2222222222y + y2 = 0 + 0.02777777778

Combine like terms: 0 + 0.02777777778 = 0.02777777778
0.2222222222y + y2 = 0.02777777778

The y term is 0.2222222222y.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222y + 0.01234567901 + y2 = 0.02777777778 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222y + y2 = 0.02777777778 + 0.01234567901

Combine like terms: 0.02777777778 + 0.01234567901 = 0.04012345679
0.01234567901 + 0.2222222222y + y2 = 0.04012345679

Factor a perfect square on the left side:
(y + 0.1111111111)(y + 0.1111111111) = 0.04012345679

Calculate the square root of the right side: 0.200308404

Break this problem into two subproblems by setting 
(y + 0.1111111111) equal to 0.200308404 and -0.200308404.


Subproblem 1
y + 0.1111111111 = 0.200308404

Simplifying
y + 0.1111111111 = 0.200308404

Reorder the terms:
0.1111111111 + y = 0.200308404

Solving
0.1111111111 + y = 0.200308404

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + y = 0.200308404 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + y = 0.200308404 + -0.1111111111
y = 0.200308404 + -0.1111111111

Combine like terms: 0.200308404 + -0.1111111111 = 0.0891972929
y = 0.0891972929

Simplifying
y = 0.0891972929


Subproblem 2
y + 0.1111111111 = -0.200308404

Simplifying
y + 0.1111111111 = -0.200308404

Reorder the terms:
0.1111111111 + y = -0.200308404

Solving
0.1111111111 + y = -0.200308404

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + y = -0.200308404 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + y = -0.200308404 + -0.1111111111
y = -0.200308404 + -0.1111111111

Combine like terms: -0.200308404 + -0.1111111111 = -0.3114195151
y = -0.3114195151

Simplifying
y = -0.3114195151


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.0891972929, -0.3114195151}

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