v^2+4v+2=18.25

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Solution for v^2+4v+2=18.25 equation: 


Simplifying
v2 + 4v + 2 = 18.25

Reorder the terms:
2 + 4v + v2 = 18.25

Solving
2 + 4v + v2 = 18.25

Solving for variable 'v'.

Reorder the terms:
2 + -18.25 + 4v + v2 = 18.25 + -18.25

Combine like terms: 2 + -18.25 = -16.25
-16.25 + 4v + v2 = 18.25 + -18.25

Combine like terms: 18.25 + -18.25 = 0.00
-16.25 + 4v + v2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '16.25' to each side of the equation.
-16.25 + 4v + 16.25 + v2 = 0.00 + 16.25

Reorder the terms:
-16.25 + 16.25 + 4v + v2 = 0.00 + 16.25

Combine like terms: -16.25 + 16.25 = 0.00
0.00 + 4v + v2 = 0.00 + 16.25
4v + v2 = 0.00 + 16.25

Combine like terms: 0.00 + 16.25 = 16.25
4v + v2 = 16.25

The v term is 4v.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4v + 4 + v2 = 16.25 + 4

Reorder the terms:
4 + 4v + v2 = 16.25 + 4

Combine like terms: 16.25 + 4 = 20.25
4 + 4v + v2 = 20.25

Factor a perfect square on the left side:
(v + 2)(v + 2) = 20.25

Calculate the square root of the right side: 4.5

Break this problem into two subproblems by setting 
(v + 2) equal to 4.5 and -4.5.


Subproblem 1
v + 2 = 4.5

Simplifying
v + 2 = 4.5

Reorder the terms:
2 + v = 4.5

Solving
2 + v = 4.5

Solving for variable 'v'.

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

Add '-2' to each side of the equation.
2 + -2 + v = 4.5 + -2

Combine like terms: 2 + -2 = 0
0 + v = 4.5 + -2
v = 4.5 + -2

Combine like terms: 4.5 + -2 = 2.5
v = 2.5

Simplifying
v = 2.5


Subproblem 2
v + 2 = -4.5

Simplifying
v + 2 = -4.5

Reorder the terms:
2 + v = -4.5

Solving
2 + v = -4.5

Solving for variable 'v'.

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

Add '-2' to each side of the equation.
2 + -2 + v = -4.5 + -2

Combine like terms: 2 + -2 = 0
0 + v = -4.5 + -2
v = -4.5 + -2

Combine like terms: -4.5 + -2 = -6.5
v = -6.5

Simplifying
v = -6.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.5, -6.5}

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