(V^2+2)=2V^2-5V+22

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Solution for (V^2+2)=2V^2-5V+22 equation: 


Simplifying
(V2 + 2) = 2V2 + -5V + 22

Reorder the terms:
(2 + V2) = 2V2 + -5V + 22

Remove parenthesis around (2 + V2)
2 + V2 = 2V2 + -5V + 22

Reorder the terms:
2 + V2 = 22 + -5V + 2V2

Solving
2 + V2 = 22 + -5V + 2V2

Solving for variable 'V'.

Reorder the terms:
2 + -22 + 5V + V2 + -2V2 = 22 + -5V + 2V2 + -22 + 5V + -2V2

Combine like terms: 2 + -22 = -20
-20 + 5V + V2 + -2V2 = 22 + -5V + 2V2 + -22 + 5V + -2V2

Combine like terms: V2 + -2V2 = -1V2
-20 + 5V + -1V2 = 22 + -5V + 2V2 + -22 + 5V + -2V2

Reorder the terms:
-20 + 5V + -1V2 = 22 + -22 + -5V + 5V + 2V2 + -2V2

Combine like terms: 22 + -22 = 0
-20 + 5V + -1V2 = 0 + -5V + 5V + 2V2 + -2V2
-20 + 5V + -1V2 = -5V + 5V + 2V2 + -2V2

Combine like terms: -5V + 5V = 0
-20 + 5V + -1V2 = 0 + 2V2 + -2V2
-20 + 5V + -1V2 = 2V2 + -2V2

Combine like terms: 2V2 + -2V2 = 0
-20 + 5V + -1V2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
20 + -5V + V2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -5V + -20 + V2 = 0 + -20

Reorder the terms:
20 + -20 + -5V + V2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -5V + V2 = 0 + -20
-5V + V2 = 0 + -20

Combine like terms: 0 + -20 = -20
-5V + V2 = -20

The V term is -5V.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5V + 6.25 + V2 = -20 + 6.25

Reorder the terms:
6.25 + -5V + V2 = -20 + 6.25

Combine like terms: -20 + 6.25 = -13.75
6.25 + -5V + V2 = -13.75

Factor a perfect square on the left side:
(V + -2.5)(V + -2.5) = -13.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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