v^2+7v-5=0

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Solution for v^2+7v-5=0 equation: 


Simplifying
v2 + 7v + -5 = 0

Reorder the terms:
-5 + 7v + v2 = 0

Solving
-5 + 7v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 7v + 5 + v2 = 0 + 5

Reorder the terms:
-5 + 5 + 7v + v2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 7v + v2 = 0 + 5
7v + v2 = 0 + 5

Combine like terms: 0 + 5 = 5
7v + v2 = 5

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 = 5 + 12.25

Reorder the terms:
12.25 + 7v + v2 = 5 + 12.25

Combine like terms: 5 + 12.25 = 17.25
12.25 + 7v + v2 = 17.25

Factor a perfect square on the left side:
(v + 3.5)(v + 3.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(v + 3.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
v + 3.5 = 4.153311931

Simplifying
v + 3.5 = 4.153311931

Reorder the terms:
3.5 + v = 4.153311931

Solving
3.5 + v = 4.153311931

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 = 4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + v = 4.153311931 + -3.5
v = 4.153311931 + -3.5

Combine like terms: 4.153311931 + -3.5 = 0.653311931
v = 0.653311931

Simplifying
v = 0.653311931


Subproblem 2
v + 3.5 = -4.153311931

Simplifying
v + 3.5 = -4.153311931

Reorder the terms:
3.5 + v = -4.153311931

Solving
3.5 + v = -4.153311931

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 = -4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + v = -4.153311931 + -3.5
v = -4.153311931 + -3.5

Combine like terms: -4.153311931 + -3.5 = -7.653311931
v = -7.653311931

Simplifying
v = -7.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.653311931, -7.653311931}

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