Y^2-10Y-25=0

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Solution for Y^2-10Y-25=0 equation: 


Simplifying
Y2 + -10Y + -25 = 0

Reorder the terms:
-25 + -10Y + Y2 = 0

Solving
-25 + -10Y + Y2 = 0

Solving for variable 'Y'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -10Y + 25 + Y2 = 0 + 25

Reorder the terms:
-25 + 25 + -10Y + Y2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -10Y + Y2 = 0 + 25
-10Y + Y2 = 0 + 25

Combine like terms: 0 + 25 = 25
-10Y + Y2 = 25

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 = 25 + 25

Reorder the terms:
25 + -10Y + Y2 = 25 + 25

Combine like terms: 25 + 25 = 50
25 + -10Y + Y2 = 50

Factor a perfect square on the left side:
(Y + -5)(Y + -5) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(Y + -5) equal to 7.071067812 and -7.071067812.


Subproblem 1
Y + -5 = 7.071067812

Simplifying
Y + -5 = 7.071067812

Reorder the terms:
-5 + Y = 7.071067812

Solving
-5 + Y = 7.071067812

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 = 7.071067812 + 5

Combine like terms: -5 + 5 = 0
0 + Y = 7.071067812 + 5
Y = 7.071067812 + 5

Combine like terms: 7.071067812 + 5 = 12.071067812
Y = 12.071067812

Simplifying
Y = 12.071067812


Subproblem 2
Y + -5 = -7.071067812

Simplifying
Y + -5 = -7.071067812

Reorder the terms:
-5 + Y = -7.071067812

Solving
-5 + Y = -7.071067812

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 = -7.071067812 + 5

Combine like terms: -5 + 5 = 0
0 + Y = -7.071067812 + 5
Y = -7.071067812 + 5

Combine like terms: -7.071067812 + 5 = -2.071067812
Y = -2.071067812

Simplifying
Y = -2.071067812


Solution
The solution to the problem is based on the solutions
from the subproblems.
Y = {12.071067812, -2.071067812}

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