v^2-16v-33=0

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Solution for v^2-16v-33=0 equation: 


Simplifying
v2 + -16v + -33 = 0

Reorder the terms:
-33 + -16v + v2 = 0

Solving
-33 + -16v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -16v + 33 + v2 = 0 + 33

Reorder the terms:
-33 + 33 + -16v + v2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -16v + v2 = 0 + 33
-16v + v2 = 0 + 33

Combine like terms: 0 + 33 = 33
-16v + v2 = 33

The v term is -16v.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16v + 64 + v2 = 33 + 64

Reorder the terms:
64 + -16v + v2 = 33 + 64

Combine like terms: 33 + 64 = 97
64 + -16v + v2 = 97

Factor a perfect square on the left side:
(v + -8)(v + -8) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(v + -8) equal to 9.848857802 and -9.848857802.


Subproblem 1
v + -8 = 9.848857802

Simplifying
v + -8 = 9.848857802

Reorder the terms:
-8 + v = 9.848857802

Solving
-8 + v = 9.848857802

Solving for variable 'v'.

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

Add '8' to each side of the equation.
-8 + 8 + v = 9.848857802 + 8

Combine like terms: -8 + 8 = 0
0 + v = 9.848857802 + 8
v = 9.848857802 + 8

Combine like terms: 9.848857802 + 8 = 17.848857802
v = 17.848857802

Simplifying
v = 17.848857802


Subproblem 2
v + -8 = -9.848857802

Simplifying
v + -8 = -9.848857802

Reorder the terms:
-8 + v = -9.848857802

Solving
-8 + v = -9.848857802

Solving for variable 'v'.

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

Add '8' to each side of the equation.
-8 + 8 + v = -9.848857802 + 8

Combine like terms: -8 + 8 = 0
0 + v = -9.848857802 + 8
v = -9.848857802 + 8

Combine like terms: -9.848857802 + 8 = -1.848857802
v = -1.848857802

Simplifying
v = -1.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {17.848857802, -1.848857802}

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