v^2+9v-14=0

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Solution for v^2+9v-14=0 equation: 


Simplifying
v2 + 9v + -14 = 0

Reorder the terms:
-14 + 9v + v2 = 0

Solving
-14 + 9v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 9v + 14 + v2 = 0 + 14

Reorder the terms:
-14 + 14 + 9v + v2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 9v + v2 = 0 + 14
9v + v2 = 0 + 14

Combine like terms: 0 + 14 = 14
9v + v2 = 14

The v term is 9v.  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.
9v + 20.25 + v2 = 14 + 20.25

Reorder the terms:
20.25 + 9v + v2 = 14 + 20.25

Combine like terms: 14 + 20.25 = 34.25
20.25 + 9v + v2 = 34.25

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

Calculate the square root of the right side: 5.852349955

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


Subproblem 1
v + 4.5 = 5.852349955

Simplifying
v + 4.5 = 5.852349955

Reorder the terms:
4.5 + v = 5.852349955

Solving
4.5 + v = 5.852349955

Solving for variable 'v'.

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

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

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

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

Simplifying
v = 1.352349955


Subproblem 2
v + 4.5 = -5.852349955

Simplifying
v + 4.5 = -5.852349955

Reorder the terms:
4.5 + v = -5.852349955

Solving
4.5 + v = -5.852349955

Solving for variable 'v'.

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

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

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

Combine like terms: -5.852349955 + -4.5 = -10.352349955
v = -10.352349955

Simplifying
v = -10.352349955


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

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