(y-5)(y-2)=25

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Solution for (y-5)(y-2)=25 equation: 


Simplifying
(y + -5)(y + -2) = 25

Reorder the terms:
(-5 + y)(y + -2) = 25

Reorder the terms:
(-5 + y)(-2 + y) = 25

Multiply (-5 + y) * (-2 + y)
(-5(-2 + y) + y(-2 + y)) = 25
((-2 * -5 + y * -5) + y(-2 + y)) = 25
((10 + -5y) + y(-2 + y)) = 25
(10 + -5y + (-2 * y + y * y)) = 25
(10 + -5y + (-2y + y2)) = 25

Combine like terms: -5y + -2y = -7y
(10 + -7y + y2) = 25

Solving
10 + -7y + y2 = 25

Solving for variable 'y'.

Reorder the terms:
10 + -25 + -7y + y2 = 25 + -25

Combine like terms: 10 + -25 = -15
-15 + -7y + y2 = 25 + -25

Combine like terms: 25 + -25 = 0
-15 + -7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -7y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + -7y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -7y + y2 = 0 + 15
-7y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
-7y + y2 = 15

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = 15 + 12.25

Reorder the terms:
12.25 + -7y + y2 = 15 + 12.25

Combine like terms: 15 + 12.25 = 27.25
12.25 + -7y + y2 = 27.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(y + -3.5) equal to 5.220153254 and -5.220153254.


Subproblem 1
y + -3.5 = 5.220153254

Simplifying
y + -3.5 = 5.220153254

Reorder the terms:
-3.5 + y = 5.220153254

Solving
-3.5 + y = 5.220153254

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 5.220153254 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 5.220153254 + 3.5
y = 5.220153254 + 3.5

Combine like terms: 5.220153254 + 3.5 = 8.720153254
y = 8.720153254

Simplifying
y = 8.720153254


Subproblem 2
y + -3.5 = -5.220153254

Simplifying
y + -3.5 = -5.220153254

Reorder the terms:
-3.5 + y = -5.220153254

Solving
-3.5 + y = -5.220153254

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -5.220153254 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -5.220153254 + 3.5
y = -5.220153254 + 3.5

Combine like terms: -5.220153254 + 3.5 = -1.720153254
y = -1.720153254

Simplifying
y = -1.720153254


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.720153254, -1.720153254}

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