y^2+0.1778y-0.3696=0

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Solution for y^2+0.1778y-0.3696=0 equation: 


Simplifying
y2 + 0.1778y + -0.3696 = 0

Reorder the terms:
-0.3696 + 0.1778y + y2 = 0

Solving
-0.3696 + 0.1778y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '0.3696' to each side of the equation.
-0.3696 + 0.1778y + 0.3696 + y2 = 0 + 0.3696

Reorder the terms:
-0.3696 + 0.3696 + 0.1778y + y2 = 0 + 0.3696

Combine like terms: -0.3696 + 0.3696 = 0.0000
0.0000 + 0.1778y + y2 = 0 + 0.3696
0.1778y + y2 = 0 + 0.3696

Combine like terms: 0 + 0.3696 = 0.3696
0.1778y + y2 = 0.3696

The y term is 0.1778y.  Take half its coefficient (0.0889).
Square it (0.00790321) and add it to both sides.

Add '0.00790321' to each side of the equation.
0.1778y + 0.00790321 + y2 = 0.3696 + 0.00790321

Reorder the terms:
0.00790321 + 0.1778y + y2 = 0.3696 + 0.00790321

Combine like terms: 0.3696 + 0.00790321 = 0.37750321
0.00790321 + 0.1778y + y2 = 0.37750321

Factor a perfect square on the left side:
(y + 0.0889)(y + 0.0889) = 0.37750321

Calculate the square root of the right side: 0.614412899

Break this problem into two subproblems by setting 
(y + 0.0889) equal to 0.614412899 and -0.614412899.


Subproblem 1
y + 0.0889 = 0.614412899

Simplifying
y + 0.0889 = 0.614412899

Reorder the terms:
0.0889 + y = 0.614412899

Solving
0.0889 + y = 0.614412899

Solving for variable 'y'.

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

Add '-0.0889' to each side of the equation.
0.0889 + -0.0889 + y = 0.614412899 + -0.0889

Combine like terms: 0.0889 + -0.0889 = 0.0000
0.0000 + y = 0.614412899 + -0.0889
y = 0.614412899 + -0.0889

Combine like terms: 0.614412899 + -0.0889 = 0.525512899
y = 0.525512899

Simplifying
y = 0.525512899


Subproblem 2
y + 0.0889 = -0.614412899

Simplifying
y + 0.0889 = -0.614412899

Reorder the terms:
0.0889 + y = -0.614412899

Solving
0.0889 + y = -0.614412899

Solving for variable 'y'.

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

Add '-0.0889' to each side of the equation.
0.0889 + -0.0889 + y = -0.614412899 + -0.0889

Combine like terms: 0.0889 + -0.0889 = 0.0000
0.0000 + y = -0.614412899 + -0.0889
y = -0.614412899 + -0.0889

Combine like terms: -0.614412899 + -0.0889 = -0.703312899
y = -0.703312899

Simplifying
y = -0.703312899


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.525512899, -0.703312899}

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