Y^2+15Y-2=0

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Solution for Y^2+15Y-2=0 equation: 


Simplifying
Y2 + 15Y + -2 = 0

Reorder the terms:
-2 + 15Y + Y2 = 0

Solving
-2 + 15Y + Y2 = 0

Solving for variable 'Y'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 15Y + 2 + Y2 = 0 + 2

Reorder the terms:
-2 + 2 + 15Y + Y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 15Y + Y2 = 0 + 2
15Y + Y2 = 0 + 2

Combine like terms: 0 + 2 = 2
15Y + Y2 = 2

The Y term is 15Y.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15Y + 56.25 + Y2 = 2 + 56.25

Reorder the terms:
56.25 + 15Y + Y2 = 2 + 56.25

Combine like terms: 2 + 56.25 = 58.25
56.25 + 15Y + Y2 = 58.25

Factor a perfect square on the left side:
(Y + 7.5)(Y + 7.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(Y + 7.5) equal to 7.632168761 and -7.632168761.


Subproblem 1
Y + 7.5 = 7.632168761

Simplifying
Y + 7.5 = 7.632168761

Reorder the terms:
7.5 + Y = 7.632168761

Solving
7.5 + Y = 7.632168761

Solving for variable 'Y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + Y = 7.632168761 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + Y = 7.632168761 + -7.5
Y = 7.632168761 + -7.5

Combine like terms: 7.632168761 + -7.5 = 0.132168761
Y = 0.132168761

Simplifying
Y = 0.132168761


Subproblem 2
Y + 7.5 = -7.632168761

Simplifying
Y + 7.5 = -7.632168761

Reorder the terms:
7.5 + Y = -7.632168761

Solving
7.5 + Y = -7.632168761

Solving for variable 'Y'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + Y = -7.632168761 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + Y = -7.632168761 + -7.5
Y = -7.632168761 + -7.5

Combine like terms: -7.632168761 + -7.5 = -15.132168761
Y = -15.132168761

Simplifying
Y = -15.132168761


Solution
The solution to the problem is based on the solutions
from the subproblems.
Y = {0.132168761, -15.132168761}

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