v^2-13v+4=0

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Solution for v^2-13v+4=0 equation: 


Simplifying
v2 + -13v + 4 = 0

Reorder the terms:
4 + -13v + v2 = 0

Solving
4 + -13v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -13v + -4 + v2 = 0 + -4

Reorder the terms:
4 + -4 + -13v + v2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -13v + v2 = 0 + -4
-13v + v2 = 0 + -4

Combine like terms: 0 + -4 = -4
-13v + v2 = -4

The v term is -13v.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13v + 42.25 + v2 = -4 + 42.25

Reorder the terms:
42.25 + -13v + v2 = -4 + 42.25

Combine like terms: -4 + 42.25 = 38.25
42.25 + -13v + v2 = 38.25

Factor a perfect square on the left side:
(v + -6.5)(v + -6.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(v + -6.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
v + -6.5 = 6.184658438

Simplifying
v + -6.5 = 6.184658438

Reorder the terms:
-6.5 + v = 6.184658438

Solving
-6.5 + v = 6.184658438

Solving for variable 'v'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + v = 6.184658438 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + v = 6.184658438 + 6.5
v = 6.184658438 + 6.5

Combine like terms: 6.184658438 + 6.5 = 12.684658438
v = 12.684658438

Simplifying
v = 12.684658438


Subproblem 2
v + -6.5 = -6.184658438

Simplifying
v + -6.5 = -6.184658438

Reorder the terms:
-6.5 + v = -6.184658438

Solving
-6.5 + v = -6.184658438

Solving for variable 'v'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + v = -6.184658438 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + v = -6.184658438 + 6.5
v = -6.184658438 + 6.5

Combine like terms: -6.184658438 + 6.5 = 0.315341562
v = 0.315341562

Simplifying
v = 0.315341562


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {12.684658438, 0.315341562}

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