v^2-9v=2

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Solution for v^2-9v=2 equation: 


Simplifying
v2 + -9v = 2

Reorder the terms:
-9v + v2 = 2

Solving
-9v + v2 = 2

Solving for variable 'v'.

Reorder the terms:
-2 + -9v + v2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -9v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -9v + 2 + v2 = 0 + 2

Reorder the terms:
-2 + 2 + -9v + v2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -9v + v2 = 0 + 2
-9v + v2 = 0 + 2

Combine like terms: 0 + 2 = 2
-9v + v2 = 2

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 = 2 + 20.25

Reorder the terms:
20.25 + -9v + v2 = 2 + 20.25

Combine like terms: 2 + 20.25 = 22.25
20.25 + -9v + v2 = 22.25

Factor a perfect square on the left side:
(v + -4.5)(v + -4.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(v + -4.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
v + -4.5 = 4.716990566

Simplifying
v + -4.5 = 4.716990566

Reorder the terms:
-4.5 + v = 4.716990566

Solving
-4.5 + v = 4.716990566

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 = 4.716990566 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + v = 4.716990566 + 4.5
v = 4.716990566 + 4.5

Combine like terms: 4.716990566 + 4.5 = 9.216990566
v = 9.216990566

Simplifying
v = 9.216990566


Subproblem 2
v + -4.5 = -4.716990566

Simplifying
v + -4.5 = -4.716990566

Reorder the terms:
-4.5 + v = -4.716990566

Solving
-4.5 + v = -4.716990566

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 = -4.716990566 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + v = -4.716990566 + 4.5
v = -4.716990566 + 4.5

Combine like terms: -4.716990566 + 4.5 = -0.216990566
v = -0.216990566

Simplifying
v = -0.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {9.216990566, -0.216990566}

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