v^2+7v-2=0

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Solution for v^2+7v-2=0 equation: 


Simplifying
v2 + 7v + -2 = 0

Reorder the terms:
-2 + 7v + v2 = 0

Solving
-2 + 7v + 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 + 7v + 2 + v2 = 0 + 2

Reorder the terms:
-2 + 2 + 7v + v2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7v + v2 = 0 + 2
7v + v2 = 0 + 2

Combine like terms: 0 + 2 = 2
7v + v2 = 2

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 = 2 + 12.25

Reorder the terms:
12.25 + 7v + v2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + 7v + v2 = 14.25

Factor a perfect square on the left side:
(v + 3.5)(v + 3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(v + 3.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
v + 3.5 = 3.774917218

Simplifying
v + 3.5 = 3.774917218

Reorder the terms:
3.5 + v = 3.774917218

Solving
3.5 + v = 3.774917218

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 = 3.774917218 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + v = 3.774917218 + -3.5
v = 3.774917218 + -3.5

Combine like terms: 3.774917218 + -3.5 = 0.274917218
v = 0.274917218

Simplifying
v = 0.274917218


Subproblem 2
v + 3.5 = -3.774917218

Simplifying
v + 3.5 = -3.774917218

Reorder the terms:
3.5 + v = -3.774917218

Solving
3.5 + v = -3.774917218

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 = -3.774917218 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + v = -3.774917218 + -3.5
v = -3.774917218 + -3.5

Combine like terms: -3.774917218 + -3.5 = -7.274917218
v = -7.274917218

Simplifying
v = -7.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.274917218, -7.274917218}

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