y^2+y-14=0

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


Simplifying
y2 + y + -14 = 0

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

Solving
-14 + y + 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 + y + 14 + y2 = 0 + 14

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

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

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

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
y + 0.25 + y2 = 14 + 0.25

Reorder the terms:
0.25 + y + y2 = 14 + 0.25

Combine like terms: 14 + 0.25 = 14.25
0.25 + y + y2 = 14.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(y + 0.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
y + 0.5 = 3.774917218

Simplifying
y + 0.5 = 3.774917218

Reorder the terms:
0.5 + y = 3.774917218

Solving
0.5 + y = 3.774917218

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 3.774917218 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 3.774917218 + -0.5
y = 3.774917218 + -0.5

Combine like terms: 3.774917218 + -0.5 = 3.274917218
y = 3.274917218

Simplifying
y = 3.274917218


Subproblem 2
y + 0.5 = -3.774917218

Simplifying
y + 0.5 = -3.774917218

Reorder the terms:
0.5 + y = -3.774917218

Solving
0.5 + y = -3.774917218

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -3.774917218 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -3.774917218 + -0.5
y = -3.774917218 + -0.5

Combine like terms: -3.774917218 + -0.5 = -4.274917218
y = -4.274917218

Simplifying
y = -4.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.274917218, -4.274917218}

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