v^2+9v=18

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Solution for v^2+9v=18 equation: 


Simplifying
v2 + 9v = 18

Reorder the terms:
9v + v2 = 18

Solving
9v + v2 = 18

Solving for variable 'v'.

Reorder the terms:
-18 + 9v + v2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 9v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 9v + 18 + v2 = 0 + 18

Reorder the terms:
-18 + 18 + 9v + v2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 9v + v2 = 0 + 18
9v + v2 = 0 + 18

Combine like terms: 0 + 18 = 18
9v + v2 = 18

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 = 18 + 20.25

Reorder the terms:
20.25 + 9v + v2 = 18 + 20.25

Combine like terms: 18 + 20.25 = 38.25
20.25 + 9v + v2 = 38.25

Factor a perfect square on the left side:
(v + 4.5)(v + 4.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(v + 4.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
v + 4.5 = 6.184658438

Simplifying
v + 4.5 = 6.184658438

Reorder the terms:
4.5 + v = 6.184658438

Solving
4.5 + v = 6.184658438

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 = 6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + v = 6.184658438 + -4.5
v = 6.184658438 + -4.5

Combine like terms: 6.184658438 + -4.5 = 1.684658438
v = 1.684658438

Simplifying
v = 1.684658438


Subproblem 2
v + 4.5 = -6.184658438

Simplifying
v + 4.5 = -6.184658438

Reorder the terms:
4.5 + v = -6.184658438

Solving
4.5 + v = -6.184658438

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 = -6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + v = -6.184658438 + -4.5
v = -6.184658438 + -4.5

Combine like terms: -6.184658438 + -4.5 = -10.684658438
v = -10.684658438

Simplifying
v = -10.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.684658438, -10.684658438}

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