v^2-16v-41=0

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Solution for v^2-16v-41=0 equation:


Simplifying
v2 + -16v + -41 = 0

Reorder the terms:
-41 + -16v + v2 = 0

Solving
-41 + -16v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -16v + 41 + v2 = 0 + 41

Reorder the terms:
-41 + 41 + -16v + v2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -16v + v2 = 0 + 41
-16v + v2 = 0 + 41

Combine like terms: 0 + 41 = 41
-16v + v2 = 41

The v term is -16v.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16v + 64 + v2 = 41 + 64

Reorder the terms:
64 + -16v + v2 = 41 + 64

Combine like terms: 41 + 64 = 105
64 + -16v + v2 = 105

Factor a perfect square on the left side:
(v + -8)(v + -8) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(v + -8) equal to 10.246950766 and -10.246950766.


Subproblem 1
v + -8 = 10.246950766

Simplifying
v + -8 = 10.246950766

Reorder the terms:
-8 + v = 10.246950766

Solving
-8 + v = 10.246950766

Solving for variable 'v'.

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

Add '8' to each side of the equation.
-8 + 8 + v = 10.246950766 + 8

Combine like terms: -8 + 8 = 0
0 + v = 10.246950766 + 8
v = 10.246950766 + 8

Combine like terms: 10.246950766 + 8 = 18.246950766
v = 18.246950766

Simplifying
v = 18.246950766


Subproblem 2
v + -8 = -10.246950766

Simplifying
v + -8 = -10.246950766

Reorder the terms:
-8 + v = -10.246950766

Solving
-8 + v = -10.246950766

Solving for variable 'v'.

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

Add '8' to each side of the equation.
-8 + 8 + v = -10.246950766 + 8

Combine like terms: -8 + 8 = 0
0 + v = -10.246950766 + 8
v = -10.246950766 + 8

Combine like terms: -10.246950766 + 8 = -2.246950766
v = -2.246950766

Simplifying
v = -2.246950766


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {18.246950766, -2.246950766}

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