y^2+10y-4=0

Solution for y^2+10y-4=0 equation:

Simplifying
y2 + 10y + -4 = 0

Reorder the terms:
-4 + 10y + y2 = 0

Solving
-4 + 10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 10y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 10y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 10y + y2 = 0 + 4
10y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
10y + y2 = 4

The y term is 10y.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10y + 25 + y2 = 4 + 25

Reorder the terms:
25 + 10y + y2 = 4 + 25

Combine like terms: 4 + 25 = 29
25 + 10y + y2 = 29

Factor a perfect square on the left side:
(y + 5)(y + 5) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(y + 5) equal to 5.385164807 and -5.385164807.

Subproblem 1
y + 5 = 5.385164807

Simplifying
y + 5 = 5.385164807

Reorder the terms:
5 + y = 5.385164807

Solving
5 + y = 5.385164807

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = 5.385164807 + -5

Combine like terms: 5 + -5 = 0
0 + y = 5.385164807 + -5
y = 5.385164807 + -5

Combine like terms: 5.385164807 + -5 = 0.385164807
y = 0.385164807

Simplifying
y = 0.385164807

Subproblem 2
y + 5 = -5.385164807

Simplifying
y + 5 = -5.385164807

Reorder the terms:
5 + y = -5.385164807

Solving
5 + y = -5.385164807

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = -5.385164807 + -5

Combine like terms: 5 + -5 = 0
0 + y = -5.385164807 + -5
y = -5.385164807 + -5

Combine like terms: -5.385164807 + -5 = -10.385164807
y = -10.385164807

Simplifying
y = -10.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.385164807, -10.385164807}