5y^2-125y+50=0

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Solution for 5y^2-125y+50=0 equation: 


Simplifying
5y2 + -125y + 50 = 0

Reorder the terms:
50 + -125y + 5y2 = 0

Solving
50 + -125y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(10 + -25y + y2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(10 + -25y + y2)' equal to zero and attempt to solve:

Simplifying
10 + -25y + y2 = 0

Solving
10 + -25y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -25y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + -25y + y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -25y + y2 = 0 + -10
-25y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
-25y + y2 = -10

The y term is -25y.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25y + 156.25 + y2 = -10 + 156.25

Reorder the terms:
156.25 + -25y + y2 = -10 + 156.25

Combine like terms: -10 + 156.25 = 146.25
156.25 + -25y + y2 = 146.25

Factor a perfect square on the left side:
(y + -12.5)(y + -12.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(y + -12.5) equal to 12.093386622 and -12.093386622.


Subproblem 1
y + -12.5 = 12.093386622

Simplifying
y + -12.5 = 12.093386622

Reorder the terms:
-12.5 + y = 12.093386622

Solving
-12.5 + y = 12.093386622

Solving for variable 'y'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + y = 12.093386622 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + y = 12.093386622 + 12.5
y = 12.093386622 + 12.5

Combine like terms: 12.093386622 + 12.5 = 24.593386622
y = 24.593386622

Simplifying
y = 24.593386622


Subproblem 2
y + -12.5 = -12.093386622

Simplifying
y + -12.5 = -12.093386622

Reorder the terms:
-12.5 + y = -12.093386622

Solving
-12.5 + y = -12.093386622

Solving for variable 'y'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + y = -12.093386622 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + y = -12.093386622 + 12.5
y = -12.093386622 + 12.5

Combine like terms: -12.093386622 + 12.5 = 0.406613378
y = 0.406613378

Simplifying
y = 0.406613378


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {24.593386622, 0.406613378}
Solution
y = {24.593386622, 0.406613378}

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