2y(y+25)=28

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Solution for 2y(y+25)=28 equation: 


Simplifying
2y(y + 25) = 28

Reorder the terms:
2y(25 + y) = 28
(25 * 2y + y * 2y) = 28
(50y + 2y2) = 28

Solving
50y + 2y2 = 28

Solving for variable 'y'.

Reorder the terms:
-28 + 50y + 2y2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 50y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 25y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + 25y + y2)' equal to zero and attempt to solve:

Simplifying
-14 + 25y + y2 = 0

Solving
-14 + 25y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 25y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + 25y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 25y + y2 = 0 + 14
25y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
25y + y2 = 14

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 = 14 + 156.25

Reorder the terms:
156.25 + 25y + y2 = 14 + 156.25

Combine like terms: 14 + 156.25 = 170.25
156.25 + 25y + y2 = 170.25

Factor a perfect square on the left side:
(y + 12.5)(y + 12.5) = 170.25

Calculate the square root of the right side: 13.047988351

Break this problem into two subproblems by setting 
(y + 12.5) equal to 13.047988351 and -13.047988351.


Subproblem 1
y + 12.5 = 13.047988351

Simplifying
y + 12.5 = 13.047988351

Reorder the terms:
12.5 + y = 13.047988351

Solving
12.5 + y = 13.047988351

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 = 13.047988351 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + y = 13.047988351 + -12.5
y = 13.047988351 + -12.5

Combine like terms: 13.047988351 + -12.5 = 0.547988351
y = 0.547988351

Simplifying
y = 0.547988351


Subproblem 2
y + 12.5 = -13.047988351

Simplifying
y + 12.5 = -13.047988351

Reorder the terms:
12.5 + y = -13.047988351

Solving
12.5 + y = -13.047988351

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 = -13.047988351 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + y = -13.047988351 + -12.5
y = -13.047988351 + -12.5

Combine like terms: -13.047988351 + -12.5 = -25.547988351
y = -25.547988351

Simplifying
y = -25.547988351


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.547988351, -25.547988351}
Solution
y = {0.547988351, -25.547988351}

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