y^2-9y-14=0

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Solution for y^2-9y-14=0 equation: 


Simplifying
y2 + -9y + -14 = 0

Reorder the terms:
-14 + -9y + y2 = 0

Solving
-14 + -9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -9y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + -9y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -9y + y2 = 0 + 14
-9y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
-9y + y2 = 14

The y term is -9y.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9y + 20.25 + y2 = 14 + 20.25

Reorder the terms:
20.25 + -9y + y2 = 14 + 20.25

Combine like terms: 14 + 20.25 = 34.25
20.25 + -9y + y2 = 34.25

Factor a perfect square on the left side:
(y + -4.5)(y + -4.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(y + -4.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
y + -4.5 = 5.852349955

Simplifying
y + -4.5 = 5.852349955

Reorder the terms:
-4.5 + y = 5.852349955

Solving
-4.5 + y = 5.852349955

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = 5.852349955 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = 5.852349955 + 4.5
y = 5.852349955 + 4.5

Combine like terms: 5.852349955 + 4.5 = 10.352349955
y = 10.352349955

Simplifying
y = 10.352349955


Subproblem 2
y + -4.5 = -5.852349955

Simplifying
y + -4.5 = -5.852349955

Reorder the terms:
-4.5 + y = -5.852349955

Solving
-4.5 + y = -5.852349955

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = -5.852349955 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = -5.852349955 + 4.5
y = -5.852349955 + 4.5

Combine like terms: -5.852349955 + 4.5 = -1.352349955
y = -1.352349955

Simplifying
y = -1.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.352349955, -1.352349955}

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