y^2+5y-5=0

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Solution for y^2+5y-5=0 equation:


Simplifying
y2 + 5y + -5 = 0

Reorder the terms:
-5 + 5y + y2 = 0

Solving
-5 + 5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 5y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 5y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 5y + y2 = 0 + 5
5y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
5y + y2 = 5

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + 5y + y2 = 11.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(y + 2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
y + 2.5 = 3.354101966

Simplifying
y + 2.5 = 3.354101966

Reorder the terms:
2.5 + y = 3.354101966

Solving
2.5 + y = 3.354101966

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 3.354101966 + -2.5
y = 3.354101966 + -2.5

Combine like terms: 3.354101966 + -2.5 = 0.854101966
y = 0.854101966

Simplifying
y = 0.854101966


Subproblem 2
y + 2.5 = -3.354101966

Simplifying
y + 2.5 = -3.354101966

Reorder the terms:
2.5 + y = -3.354101966

Solving
2.5 + y = -3.354101966

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -3.354101966 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -3.354101966 + -2.5
y = -3.354101966 + -2.5

Combine like terms: -3.354101966 + -2.5 = -5.854101966
y = -5.854101966

Simplifying
y = -5.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.854101966, -5.854101966}

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