v^2-24v+41=0

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Solution for v^2-24v+41=0 equation: 


Simplifying
v2 + -24v + 41 = 0

Reorder the terms:
41 + -24v + v2 = 0

Solving
41 + -24v + 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 + -24v + -41 + v2 = 0 + -41

Reorder the terms:
41 + -41 + -24v + v2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -24v + v2 = 0 + -41
-24v + v2 = 0 + -41

Combine like terms: 0 + -41 = -41
-24v + v2 = -41

The v term is -24v.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24v + 144 + v2 = -41 + 144

Reorder the terms:
144 + -24v + v2 = -41 + 144

Combine like terms: -41 + 144 = 103
144 + -24v + v2 = 103

Factor a perfect square on the left side:
(v + -12)(v + -12) = 103

Calculate the square root of the right side: 10.148891565

Break this problem into two subproblems by setting 
(v + -12) equal to 10.148891565 and -10.148891565.


Subproblem 1
v + -12 = 10.148891565

Simplifying
v + -12 = 10.148891565

Reorder the terms:
-12 + v = 10.148891565

Solving
-12 + v = 10.148891565

Solving for variable 'v'.

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

Add '12' to each side of the equation.
-12 + 12 + v = 10.148891565 + 12

Combine like terms: -12 + 12 = 0
0 + v = 10.148891565 + 12
v = 10.148891565 + 12

Combine like terms: 10.148891565 + 12 = 22.148891565
v = 22.148891565

Simplifying
v = 22.148891565


Subproblem 2
v + -12 = -10.148891565

Simplifying
v + -12 = -10.148891565

Reorder the terms:
-12 + v = -10.148891565

Solving
-12 + v = -10.148891565

Solving for variable 'v'.

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

Add '12' to each side of the equation.
-12 + 12 + v = -10.148891565 + 12

Combine like terms: -12 + 12 = 0
0 + v = -10.148891565 + 12
v = -10.148891565 + 12

Combine like terms: -10.148891565 + 12 = 1.851108435
v = 1.851108435

Simplifying
v = 1.851108435


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {22.148891565, 1.851108435}

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