v^2+4v-2=0

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Solution for v^2+4v-2=0 equation: 


Simplifying
v2 + 4v + -2 = 0

Reorder the terms:
-2 + 4v + v2 = 0

Solving
-2 + 4v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4v + 2 + v2 = 0 + 2

Reorder the terms:
-2 + 2 + 4v + v2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4v + v2 = 0 + 2
4v + v2 = 0 + 2

Combine like terms: 0 + 2 = 2
4v + v2 = 2

The v term is 4v.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4v + 4 + v2 = 2 + 4

Reorder the terms:
4 + 4v + v2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4v + v2 = 6

Factor a perfect square on the left side:
(v + 2)(v + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(v + 2) equal to 2.449489743 and -2.449489743.


Subproblem 1
v + 2 = 2.449489743

Simplifying
v + 2 = 2.449489743

Reorder the terms:
2 + v = 2.449489743

Solving
2 + v = 2.449489743

Solving for variable 'v'.

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

Add '-2' to each side of the equation.
2 + -2 + v = 2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + v = 2.449489743 + -2
v = 2.449489743 + -2

Combine like terms: 2.449489743 + -2 = 0.449489743
v = 0.449489743

Simplifying
v = 0.449489743


Subproblem 2
v + 2 = -2.449489743

Simplifying
v + 2 = -2.449489743

Reorder the terms:
2 + v = -2.449489743

Solving
2 + v = -2.449489743

Solving for variable 'v'.

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

Add '-2' to each side of the equation.
2 + -2 + v = -2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + v = -2.449489743 + -2
v = -2.449489743 + -2

Combine like terms: -2.449489743 + -2 = -4.449489743
v = -4.449489743

Simplifying
v = -4.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.449489743, -4.449489743}

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