V^2=5+5V

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Solution for V^2=5+5V equation: 


Simplifying
V2 = 5 + 5V

Solving
V2 = 5 + 5V

Solving for variable 'V'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 5 + 6.25

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

Combine like terms: 5 + 6.25 = 11.25
6.25 + -5V + V2 = 11.25

Factor a perfect square on the left side:
(V + -2.5)(V + -2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(V + -2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
V + -2.5 = 3.354101966

Simplifying
V + -2.5 = 3.354101966

Reorder the terms:
-2.5 + V = 3.354101966

Solving
-2.5 + V = 3.354101966

Solving for variable 'V'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + V = 3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + V = 3.354101966 + 2.5
V = 3.354101966 + 2.5

Combine like terms: 3.354101966 + 2.5 = 5.854101966
V = 5.854101966

Simplifying
V = 5.854101966


Subproblem 2
V + -2.5 = -3.354101966

Simplifying
V + -2.5 = -3.354101966

Reorder the terms:
-2.5 + V = -3.354101966

Solving
-2.5 + V = -3.354101966

Solving for variable 'V'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + V = -3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + V = -3.354101966 + 2.5
V = -3.354101966 + 2.5

Combine like terms: -3.354101966 + 2.5 = -0.854101966
V = -0.854101966

Simplifying
V = -0.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
V = {5.854101966, -0.854101966}

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