.2v*v-3v-2.25=0

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Solution for .2v*v-3v-2.25=0 equation: 


Simplifying
0.2v * v + -3v + -2.25 = 0

Multiply v * v
0.2v2 + -3v + -2.25 = 0

Reorder the terms:
-2.25 + -3v + 0.2v2 = 0

Solving
-2.25 + -3v + 0.2v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
0.2 the coefficient of the squared term: 

Divide each side by '0.2'.
-11.25 + -15v + v2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -15v + 11.25 + v2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -15v + v2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -15v + v2 = 0 + 11.25
-15v + v2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-15v + v2 = 11.25

The v term is -15v.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15v + 56.25 + v2 = 11.25 + 56.25

Reorder the terms:
56.25 + -15v + v2 = 11.25 + 56.25

Combine like terms: 11.25 + 56.25 = 67.5
56.25 + -15v + v2 = 67.5

Factor a perfect square on the left side:
(v + -7.5)(v + -7.5) = 67.5

Calculate the square root of the right side: 8.215838363

Break this problem into two subproblems by setting 
(v + -7.5) equal to 8.215838363 and -8.215838363.


Subproblem 1
v + -7.5 = 8.215838363

Simplifying
v + -7.5 = 8.215838363

Reorder the terms:
-7.5 + v = 8.215838363

Solving
-7.5 + v = 8.215838363

Solving for variable 'v'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + v = 8.215838363 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + v = 8.215838363 + 7.5
v = 8.215838363 + 7.5

Combine like terms: 8.215838363 + 7.5 = 15.715838363
v = 15.715838363

Simplifying
v = 15.715838363


Subproblem 2
v + -7.5 = -8.215838363

Simplifying
v + -7.5 = -8.215838363

Reorder the terms:
-7.5 + v = -8.215838363

Solving
-7.5 + v = -8.215838363

Solving for variable 'v'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + v = -8.215838363 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + v = -8.215838363 + 7.5
v = -8.215838363 + 7.5

Combine like terms: -8.215838363 + 7.5 = -0.715838363
v = -0.715838363

Simplifying
v = -0.715838363


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {15.715838363, -0.715838363}

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