v^2-11v-28=0

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Solution for v^2-11v-28=0 equation: 


Simplifying
v2 + -11v + -28 = 0

Reorder the terms:
-28 + -11v + v2 = 0

Solving
-28 + -11v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -11v + 28 + v2 = 0 + 28

Reorder the terms:
-28 + 28 + -11v + v2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -11v + v2 = 0 + 28
-11v + v2 = 0 + 28

Combine like terms: 0 + 28 = 28
-11v + v2 = 28

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 = 28 + 30.25

Reorder the terms:
30.25 + -11v + v2 = 28 + 30.25

Combine like terms: 28 + 30.25 = 58.25
30.25 + -11v + v2 = 58.25

Factor a perfect square on the left side:
(v + -5.5)(v + -5.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(v + -5.5) equal to 7.632168761 and -7.632168761.


Subproblem 1
v + -5.5 = 7.632168761

Simplifying
v + -5.5 = 7.632168761

Reorder the terms:
-5.5 + v = 7.632168761

Solving
-5.5 + v = 7.632168761

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 = 7.632168761 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + v = 7.632168761 + 5.5
v = 7.632168761 + 5.5

Combine like terms: 7.632168761 + 5.5 = 13.132168761
v = 13.132168761

Simplifying
v = 13.132168761


Subproblem 2
v + -5.5 = -7.632168761

Simplifying
v + -5.5 = -7.632168761

Reorder the terms:
-5.5 + v = -7.632168761

Solving
-5.5 + v = -7.632168761

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 = -7.632168761 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + v = -7.632168761 + 5.5
v = -7.632168761 + 5.5

Combine like terms: -7.632168761 + 5.5 = -2.132168761
v = -2.132168761

Simplifying
v = -2.132168761


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {13.132168761, -2.132168761}

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