4y^2-20y-100=0

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Solution for 4y^2-20y-100=0 equation: 


Simplifying
4y2 + -20y + -100 = 0

Reorder the terms:
-100 + -20y + 4y2 = 0

Solving
-100 + -20y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + -5y + y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + -5y + y2)' equal to zero and attempt to solve:

Simplifying
-25 + -5y + y2 = 0

Solving
-25 + -5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -5y + 25 + y2 = 0 + 25

Reorder the terms:
-25 + 25 + -5y + y2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -5y + y2 = 0 + 25
-5y + y2 = 0 + 25

Combine like terms: 0 + 25 = 25
-5y + y2 = 25

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = 25 + 6.25

Reorder the terms:
6.25 + -5y + y2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + -5y + y2 = 31.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(y + -2.5) equal to 5.590169944 and -5.590169944.


Subproblem 1
y + -2.5 = 5.590169944

Simplifying
y + -2.5 = 5.590169944

Reorder the terms:
-2.5 + y = 5.590169944

Solving
-2.5 + y = 5.590169944

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 5.590169944 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 5.590169944 + 2.5
y = 5.590169944 + 2.5

Combine like terms: 5.590169944 + 2.5 = 8.090169944
y = 8.090169944

Simplifying
y = 8.090169944


Subproblem 2
y + -2.5 = -5.590169944

Simplifying
y + -2.5 = -5.590169944

Reorder the terms:
-2.5 + y = -5.590169944

Solving
-2.5 + y = -5.590169944

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -5.590169944 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -5.590169944 + 2.5
y = -5.590169944 + 2.5

Combine like terms: -5.590169944 + 2.5 = -3.090169944
y = -3.090169944

Simplifying
y = -3.090169944


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.090169944, -3.090169944}
Solution
y = {8.090169944, -3.090169944}

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