-2v^2-v+11=-3v^2+6v

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Solution for -2v^2-v+11=-3v^2+6v equation: 


Simplifying
-2v2 + -1v + 11 = -3v2 + 6v

Reorder the terms:
11 + -1v + -2v2 = -3v2 + 6v

Reorder the terms:
11 + -1v + -2v2 = 6v + -3v2

Solving
11 + -1v + -2v2 = 6v + -3v2

Solving for variable 'v'.

Reorder the terms:
11 + -1v + -6v + -2v2 + 3v2 = 6v + -3v2 + -6v + 3v2

Combine like terms: -1v + -6v = -7v
11 + -7v + -2v2 + 3v2 = 6v + -3v2 + -6v + 3v2

Combine like terms: -2v2 + 3v2 = 1v2
11 + -7v + 1v2 = 6v + -3v2 + -6v + 3v2

Reorder the terms:
11 + -7v + 1v2 = 6v + -6v + -3v2 + 3v2

Combine like terms: 6v + -6v = 0
11 + -7v + 1v2 = 0 + -3v2 + 3v2
11 + -7v + 1v2 = -3v2 + 3v2

Combine like terms: -3v2 + 3v2 = 0
11 + -7v + 1v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -7v + -11 + v2 = 0 + -11

Reorder the terms:
11 + -11 + -7v + v2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -7v + v2 = 0 + -11
-7v + v2 = 0 + -11

Combine like terms: 0 + -11 = -11
-7v + v2 = -11

The v term is -7v.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7v + 12.25 + v2 = -11 + 12.25

Reorder the terms:
12.25 + -7v + v2 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + -7v + v2 = 1.25

Factor a perfect square on the left side:
(v + -3.5)(v + -3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(v + -3.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
v + -3.5 = 1.118033989

Simplifying
v + -3.5 = 1.118033989

Reorder the terms:
-3.5 + v = 1.118033989

Solving
-3.5 + v = 1.118033989

Solving for variable 'v'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + v = 1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + v = 1.118033989 + 3.5
v = 1.118033989 + 3.5

Combine like terms: 1.118033989 + 3.5 = 4.618033989
v = 4.618033989

Simplifying
v = 4.618033989


Subproblem 2
v + -3.5 = -1.118033989

Simplifying
v + -3.5 = -1.118033989

Reorder the terms:
-3.5 + v = -1.118033989

Solving
-3.5 + v = -1.118033989

Solving for variable 'v'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + v = -1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + v = -1.118033989 + 3.5
v = -1.118033989 + 3.5

Combine like terms: -1.118033989 + 3.5 = 2.381966011
v = 2.381966011

Simplifying
v = 2.381966011


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.618033989, 2.381966011}

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