v^2-16v-29=0

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Solution for v^2-16v-29=0 equation: 


Simplifying
v2 + -16v + -29 = 0

Reorder the terms:
-29 + -16v + v2 = 0

Solving
-29 + -16v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -16v + 29 + v2 = 0 + 29

Reorder the terms:
-29 + 29 + -16v + v2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -16v + v2 = 0 + 29
-16v + v2 = 0 + 29

Combine like terms: 0 + 29 = 29
-16v + v2 = 29

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 = 29 + 64

Reorder the terms:
64 + -16v + v2 = 29 + 64

Combine like terms: 29 + 64 = 93
64 + -16v + v2 = 93

Factor a perfect square on the left side:
(v + -8)(v + -8) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(v + -8) equal to 9.643650761 and -9.643650761.


Subproblem 1
v + -8 = 9.643650761

Simplifying
v + -8 = 9.643650761

Reorder the terms:
-8 + v = 9.643650761

Solving
-8 + v = 9.643650761

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 = 9.643650761 + 8

Combine like terms: -8 + 8 = 0
0 + v = 9.643650761 + 8
v = 9.643650761 + 8

Combine like terms: 9.643650761 + 8 = 17.643650761
v = 17.643650761

Simplifying
v = 17.643650761


Subproblem 2
v + -8 = -9.643650761

Simplifying
v + -8 = -9.643650761

Reorder the terms:
-8 + v = -9.643650761

Solving
-8 + v = -9.643650761

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 = -9.643650761 + 8

Combine like terms: -8 + 8 = 0
0 + v = -9.643650761 + 8
v = -9.643650761 + 8

Combine like terms: -9.643650761 + 8 = -1.643650761
v = -1.643650761

Simplifying
v = -1.643650761


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {17.643650761, -1.643650761}

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