y^2-15y-18=0

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Solution for y^2-15y-18=0 equation: 


Simplifying
y2 + -15y + -18 = 0

Reorder the terms:
-18 + -15y + y2 = 0

Solving
-18 + -15y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -15y + 18 + y2 = 0 + 18

Reorder the terms:
-18 + 18 + -15y + y2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -15y + y2 = 0 + 18
-15y + y2 = 0 + 18

Combine like terms: 0 + 18 = 18
-15y + y2 = 18

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 = 18 + 56.25

Reorder the terms:
56.25 + -15y + y2 = 18 + 56.25

Combine like terms: 18 + 56.25 = 74.25
56.25 + -15y + y2 = 74.25

Factor a perfect square on the left side:
(y + -7.5)(y + -7.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(y + -7.5) equal to 8.61684397 and -8.61684397.


Subproblem 1
y + -7.5 = 8.61684397

Simplifying
y + -7.5 = 8.61684397

Reorder the terms:
-7.5 + y = 8.61684397

Solving
-7.5 + y = 8.61684397

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 = 8.61684397 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y = 8.61684397 + 7.5
y = 8.61684397 + 7.5

Combine like terms: 8.61684397 + 7.5 = 16.11684397
y = 16.11684397

Simplifying
y = 16.11684397


Subproblem 2
y + -7.5 = -8.61684397

Simplifying
y + -7.5 = -8.61684397

Reorder the terms:
-7.5 + y = -8.61684397

Solving
-7.5 + y = -8.61684397

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 = -8.61684397 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + y = -8.61684397 + 7.5
y = -8.61684397 + 7.5

Combine like terms: -8.61684397 + 7.5 = -1.11684397
y = -1.11684397

Simplifying
y = -1.11684397


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.11684397, -1.11684397}

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