y^2+10y-8=0

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Solution for y^2+10y-8=0 equation: 


Simplifying
y2 + 10y + -8 = 0

Reorder the terms:
-8 + 10y + y2 = 0

Solving
-8 + 10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 10y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + 10y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 10y + y2 = 0 + 8
10y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
10y + y2 = 8

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 = 8 + 25

Reorder the terms:
25 + 10y + y2 = 8 + 25

Combine like terms: 8 + 25 = 33
25 + 10y + y2 = 33

Factor a perfect square on the left side:
(y + 5)(y + 5) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(y + 5) equal to 5.744562647 and -5.744562647.


Subproblem 1
y + 5 = 5.744562647

Simplifying
y + 5 = 5.744562647

Reorder the terms:
5 + y = 5.744562647

Solving
5 + y = 5.744562647

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 = 5.744562647 + -5

Combine like terms: 5 + -5 = 0
0 + y = 5.744562647 + -5
y = 5.744562647 + -5

Combine like terms: 5.744562647 + -5 = 0.744562647
y = 0.744562647

Simplifying
y = 0.744562647


Subproblem 2
y + 5 = -5.744562647

Simplifying
y + 5 = -5.744562647

Reorder the terms:
5 + y = -5.744562647

Solving
5 + y = -5.744562647

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 = -5.744562647 + -5

Combine like terms: 5 + -5 = 0
0 + y = -5.744562647 + -5
y = -5.744562647 + -5

Combine like terms: -5.744562647 + -5 = -10.744562647
y = -10.744562647

Simplifying
y = -10.744562647


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.744562647, -10.744562647}

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