-5v^2-22v+43=9-2v-11v^2

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Solution for -5v^2-22v+43=9-2v-11v^2 equation: 


Simplifying
-5v2 + -22v + 43 = 9 + -2v + -11v2

Reorder the terms:
43 + -22v + -5v2 = 9 + -2v + -11v2

Solving
43 + -22v + -5v2 = 9 + -2v + -11v2

Solving for variable 'v'.

Reorder the terms:
43 + -9 + -22v + 2v + -5v2 + 11v2 = 9 + -2v + -11v2 + -9 + 2v + 11v2

Combine like terms: 43 + -9 = 34
34 + -22v + 2v + -5v2 + 11v2 = 9 + -2v + -11v2 + -9 + 2v + 11v2

Combine like terms: -22v + 2v = -20v
34 + -20v + -5v2 + 11v2 = 9 + -2v + -11v2 + -9 + 2v + 11v2

Combine like terms: -5v2 + 11v2 = 6v2
34 + -20v + 6v2 = 9 + -2v + -11v2 + -9 + 2v + 11v2

Reorder the terms:
34 + -20v + 6v2 = 9 + -9 + -2v + 2v + -11v2 + 11v2

Combine like terms: 9 + -9 = 0
34 + -20v + 6v2 = 0 + -2v + 2v + -11v2 + 11v2
34 + -20v + 6v2 = -2v + 2v + -11v2 + 11v2

Combine like terms: -2v + 2v = 0
34 + -20v + 6v2 = 0 + -11v2 + 11v2
34 + -20v + 6v2 = -11v2 + 11v2

Combine like terms: -11v2 + 11v2 = 0
34 + -20v + 6v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -10v + 3v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + -10v + 3v2)' equal to zero and attempt to solve:

Simplifying
17 + -10v + 3v2 = 0

Solving
17 + -10v + 3v2 = 0

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

Divide each side by '3'.
5.666666667 + -3.333333333v + v2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -3.333333333v + -5.666666667 + v2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -3.333333333v + v2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -3.333333333v + v2 = 0 + -5.666666667
-3.333333333v + v2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-3.333333333v + v2 = -5.666666667

The v term is -3.333333333v.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333v + 2.777777779 + v2 = -5.666666667 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333v + v2 = -5.666666667 + 2.777777779

Combine like terms: -5.666666667 + 2.777777779 = -2.888888888
2.777777779 + -3.333333333v + v2 = -2.888888888

Factor a perfect square on the left side:
(v + -1.666666667)(v + -1.666666667) = -2.888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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