v^2-15v-32=0

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Solution for v^2-15v-32=0 equation: 


Simplifying
v2 + -15v + -32 = 0

Reorder the terms:
-32 + -15v + v2 = 0

Solving
-32 + -15v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -15v + 32 + v2 = 0 + 32

Reorder the terms:
-32 + 32 + -15v + v2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -15v + v2 = 0 + 32
-15v + v2 = 0 + 32

Combine like terms: 0 + 32 = 32
-15v + v2 = 32

The v term is -15v.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15v + 56.25 + v2 = 32 + 56.25

Reorder the terms:
56.25 + -15v + v2 = 32 + 56.25

Combine like terms: 32 + 56.25 = 88.25
56.25 + -15v + v2 = 88.25

Factor a perfect square on the left side:
(v + -7.5)(v + -7.5) = 88.25

Calculate the square root of the right side: 9.394147114

Break this problem into two subproblems by setting 
(v + -7.5) equal to 9.394147114 and -9.394147114.


Subproblem 1
v + -7.5 = 9.394147114

Simplifying
v + -7.5 = 9.394147114

Reorder the terms:
-7.5 + v = 9.394147114

Solving
-7.5 + v = 9.394147114

Solving for variable 'v'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + v = 9.394147114 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + v = 9.394147114 + 7.5
v = 9.394147114 + 7.5

Combine like terms: 9.394147114 + 7.5 = 16.894147114
v = 16.894147114

Simplifying
v = 16.894147114


Subproblem 2
v + -7.5 = -9.394147114

Simplifying
v + -7.5 = -9.394147114

Reorder the terms:
-7.5 + v = -9.394147114

Solving
-7.5 + v = -9.394147114

Solving for variable 'v'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + v = -9.394147114 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + v = -9.394147114 + 7.5
v = -9.394147114 + 7.5

Combine like terms: -9.394147114 + 7.5 = -1.894147114
v = -1.894147114

Simplifying
v = -1.894147114


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {16.894147114, -1.894147114}

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