y^2-10y-135=0

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Solution for y^2-10y-135=0 equation: 


Simplifying
y2 + -10y + -135 = 0

Reorder the terms:
-135 + -10y + y2 = 0

Solving
-135 + -10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '135' to each side of the equation.
-135 + -10y + 135 + y2 = 0 + 135

Reorder the terms:
-135 + 135 + -10y + y2 = 0 + 135

Combine like terms: -135 + 135 = 0
0 + -10y + y2 = 0 + 135
-10y + y2 = 0 + 135

Combine like terms: 0 + 135 = 135
-10y + y2 = 135

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 = 135 + 25

Reorder the terms:
25 + -10y + y2 = 135 + 25

Combine like terms: 135 + 25 = 160
25 + -10y + y2 = 160

Factor a perfect square on the left side:
(y + -5)(y + -5) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(y + -5) equal to 12.649110641 and -12.649110641.


Subproblem 1
y + -5 = 12.649110641

Simplifying
y + -5 = 12.649110641

Reorder the terms:
-5 + y = 12.649110641

Solving
-5 + y = 12.649110641

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 = 12.649110641 + 5

Combine like terms: -5 + 5 = 0
0 + y = 12.649110641 + 5
y = 12.649110641 + 5

Combine like terms: 12.649110641 + 5 = 17.649110641
y = 17.649110641

Simplifying
y = 17.649110641


Subproblem 2
y + -5 = -12.649110641

Simplifying
y + -5 = -12.649110641

Reorder the terms:
-5 + y = -12.649110641

Solving
-5 + y = -12.649110641

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 = -12.649110641 + 5

Combine like terms: -5 + 5 = 0
0 + y = -12.649110641 + 5
y = -12.649110641 + 5

Combine like terms: -12.649110641 + 5 = -7.649110641
y = -7.649110641

Simplifying
y = -7.649110641


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {17.649110641, -7.649110641}

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