y^2+10y-66=0

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Solution for y^2+10y-66=0 equation: 


Simplifying
y2 + 10y + -66 = 0

Reorder the terms:
-66 + 10y + y2 = 0

Solving
-66 + 10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 10y + 66 + y2 = 0 + 66

Reorder the terms:
-66 + 66 + 10y + y2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 10y + y2 = 0 + 66
10y + y2 = 0 + 66

Combine like terms: 0 + 66 = 66
10y + y2 = 66

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 = 66 + 25

Reorder the terms:
25 + 10y + y2 = 66 + 25

Combine like terms: 66 + 25 = 91
25 + 10y + y2 = 91

Factor a perfect square on the left side:
(y + 5)(y + 5) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(y + 5) equal to 9.539392014 and -9.539392014.


Subproblem 1
y + 5 = 9.539392014

Simplifying
y + 5 = 9.539392014

Reorder the terms:
5 + y = 9.539392014

Solving
5 + y = 9.539392014

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 = 9.539392014 + -5

Combine like terms: 5 + -5 = 0
0 + y = 9.539392014 + -5
y = 9.539392014 + -5

Combine like terms: 9.539392014 + -5 = 4.539392014
y = 4.539392014

Simplifying
y = 4.539392014


Subproblem 2
y + 5 = -9.539392014

Simplifying
y + 5 = -9.539392014

Reorder the terms:
5 + y = -9.539392014

Solving
5 + y = -9.539392014

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 = -9.539392014 + -5

Combine like terms: 5 + -5 = 0
0 + y = -9.539392014 + -5
y = -9.539392014 + -5

Combine like terms: -9.539392014 + -5 = -14.539392014
y = -14.539392014

Simplifying
y = -14.539392014


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.539392014, -14.539392014}

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