v^2+8v+1=0

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Solution for v^2+8v+1=0 equation: 


Simplifying
v2 + 8v + 1 = 0

Reorder the terms:
1 + 8v + v2 = 0

Solving
1 + 8v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 8v + -1 + v2 = 0 + -1

Reorder the terms:
1 + -1 + 8v + v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8v + v2 = 0 + -1
8v + v2 = 0 + -1

Combine like terms: 0 + -1 = -1
8v + v2 = -1

The v term is 8v.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8v + 16 + v2 = -1 + 16

Reorder the terms:
16 + 8v + v2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + 8v + v2 = 15

Factor a perfect square on the left side:
(v + 4)(v + 4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(v + 4) equal to 3.872983346 and -3.872983346.


Subproblem 1
v + 4 = 3.872983346

Simplifying
v + 4 = 3.872983346

Reorder the terms:
4 + v = 3.872983346

Solving
4 + v = 3.872983346

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = 3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + v = 3.872983346 + -4
v = 3.872983346 + -4

Combine like terms: 3.872983346 + -4 = -0.127016654
v = -0.127016654

Simplifying
v = -0.127016654


Subproblem 2
v + 4 = -3.872983346

Simplifying
v + 4 = -3.872983346

Reorder the terms:
4 + v = -3.872983346

Solving
4 + v = -3.872983346

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = -3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + v = -3.872983346 + -4
v = -3.872983346 + -4

Combine like terms: -3.872983346 + -4 = -7.872983346
v = -7.872983346

Simplifying
v = -7.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.127016654, -7.872983346}

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