v^2-11v+23=

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Solution for v^2-11v+23= equation: 


Simplifying
v2 + -11v + 23 = 0

Reorder the terms:
23 + -11v + v2 = 0

Solving
23 + -11v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + -11v + -23 + v2 = 0 + -23

Reorder the terms:
23 + -23 + -11v + v2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -11v + v2 = 0 + -23
-11v + v2 = 0 + -23

Combine like terms: 0 + -23 = -23
-11v + v2 = -23

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 = -23 + 30.25

Reorder the terms:
30.25 + -11v + v2 = -23 + 30.25

Combine like terms: -23 + 30.25 = 7.25
30.25 + -11v + v2 = 7.25

Factor a perfect square on the left side:
(v + -5.5)(v + -5.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(v + -5.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
v + -5.5 = 2.692582404

Simplifying
v + -5.5 = 2.692582404

Reorder the terms:
-5.5 + v = 2.692582404

Solving
-5.5 + v = 2.692582404

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 = 2.692582404 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + v = 2.692582404 + 5.5
v = 2.692582404 + 5.5

Combine like terms: 2.692582404 + 5.5 = 8.192582404
v = 8.192582404

Simplifying
v = 8.192582404


Subproblem 2
v + -5.5 = -2.692582404

Simplifying
v + -5.5 = -2.692582404

Reorder the terms:
-5.5 + v = -2.692582404

Solving
-5.5 + v = -2.692582404

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 = -2.692582404 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + v = -2.692582404 + 5.5
v = -2.692582404 + 5.5

Combine like terms: -2.692582404 + 5.5 = 2.807417596
v = 2.807417596

Simplifying
v = 2.807417596


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {8.192582404, 2.807417596}

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