v^2-11v+17=0

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Solution for v^2-11v+17=0 equation:


Simplifying
v2 + -11v + 17 = 0

Reorder the terms:
17 + -11v + v2 = 0

Solving
17 + -11v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -11v + -17 + v2 = 0 + -17

Reorder the terms:
17 + -17 + -11v + v2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -11v + v2 = 0 + -17
-11v + v2 = 0 + -17

Combine like terms: 0 + -17 = -17
-11v + v2 = -17

The v term is -11v.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11v + 30.25 + v2 = -17 + 30.25

Reorder the terms:
30.25 + -11v + v2 = -17 + 30.25

Combine like terms: -17 + 30.25 = 13.25
30.25 + -11v + v2 = 13.25

Factor a perfect square on the left side:
(v + -5.5)(v + -5.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(v + -5.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
v + -5.5 = 3.640054945

Simplifying
v + -5.5 = 3.640054945

Reorder the terms:
-5.5 + v = 3.640054945

Solving
-5.5 + v = 3.640054945

Solving for variable 'v'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + v = 3.640054945 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + v = 3.640054945 + 5.5
v = 3.640054945 + 5.5

Combine like terms: 3.640054945 + 5.5 = 9.140054945
v = 9.140054945

Simplifying
v = 9.140054945


Subproblem 2
v + -5.5 = -3.640054945

Simplifying
v + -5.5 = -3.640054945

Reorder the terms:
-5.5 + v = -3.640054945

Solving
-5.5 + v = -3.640054945

Solving for variable 'v'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + v = -3.640054945 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + v = -3.640054945 + 5.5
v = -3.640054945 + 5.5

Combine like terms: -3.640054945 + 5.5 = 1.859945055
v = 1.859945055

Simplifying
v = 1.859945055


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {9.140054945, 1.859945055}

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