10y^2-100y-195=0

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Solution for 10y^2-100y-195=0 equation: 


Simplifying
10y2 + -100y + -195 = 0

Reorder the terms:
-195 + -100y + 10y2 = 0

Solving
-195 + -100y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-39 + -20y + 2y2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-39 + -20y + 2y2)' equal to zero and attempt to solve:

Simplifying
-39 + -20y + 2y2 = 0

Solving
-39 + -20y + 2y2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-19.5 + -10y + y2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + -10y + 19.5 + y2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + -10y + y2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + -10y + y2 = 0 + 19.5
-10y + y2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
-10y + y2 = 19.5

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 = 19.5 + 25

Reorder the terms:
25 + -10y + y2 = 19.5 + 25

Combine like terms: 19.5 + 25 = 44.5
25 + -10y + y2 = 44.5

Factor a perfect square on the left side:
(y + -5)(y + -5) = 44.5

Calculate the square root of the right side: 6.670832032

Break this problem into two subproblems by setting 
(y + -5) equal to 6.670832032 and -6.670832032.


Subproblem 1
y + -5 = 6.670832032

Simplifying
y + -5 = 6.670832032

Reorder the terms:
-5 + y = 6.670832032

Solving
-5 + y = 6.670832032

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 = 6.670832032 + 5

Combine like terms: -5 + 5 = 0
0 + y = 6.670832032 + 5
y = 6.670832032 + 5

Combine like terms: 6.670832032 + 5 = 11.670832032
y = 11.670832032

Simplifying
y = 11.670832032


Subproblem 2
y + -5 = -6.670832032

Simplifying
y + -5 = -6.670832032

Reorder the terms:
-5 + y = -6.670832032

Solving
-5 + y = -6.670832032

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 = -6.670832032 + 5

Combine like terms: -5 + 5 = 0
0 + y = -6.670832032 + 5
y = -6.670832032 + 5

Combine like terms: -6.670832032 + 5 = -1.670832032
y = -1.670832032

Simplifying
y = -1.670832032


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.670832032, -1.670832032}
Solution
y = {11.670832032, -1.670832032}

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