v^2+30v-41=0

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Solution for v^2+30v-41=0 equation: 


Simplifying
v2 + 30v + -41 = 0

Reorder the terms:
-41 + 30v + v2 = 0

Solving
-41 + 30v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 30v + 41 + v2 = 0 + 41

Reorder the terms:
-41 + 41 + 30v + v2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 30v + v2 = 0 + 41
30v + v2 = 0 + 41

Combine like terms: 0 + 41 = 41
30v + v2 = 41

The v term is 30v.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30v + 225 + v2 = 41 + 225

Reorder the terms:
225 + 30v + v2 = 41 + 225

Combine like terms: 41 + 225 = 266
225 + 30v + v2 = 266

Factor a perfect square on the left side:
(v + 15)(v + 15) = 266

Calculate the square root of the right side: 16.30950643

Break this problem into two subproblems by setting 
(v + 15) equal to 16.30950643 and -16.30950643.


Subproblem 1
v + 15 = 16.30950643

Simplifying
v + 15 = 16.30950643

Reorder the terms:
15 + v = 16.30950643

Solving
15 + v = 16.30950643

Solving for variable 'v'.

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

Add '-15' to each side of the equation.
15 + -15 + v = 16.30950643 + -15

Combine like terms: 15 + -15 = 0
0 + v = 16.30950643 + -15
v = 16.30950643 + -15

Combine like terms: 16.30950643 + -15 = 1.30950643
v = 1.30950643

Simplifying
v = 1.30950643


Subproblem 2
v + 15 = -16.30950643

Simplifying
v + 15 = -16.30950643

Reorder the terms:
15 + v = -16.30950643

Solving
15 + v = -16.30950643

Solving for variable 'v'.

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

Add '-15' to each side of the equation.
15 + -15 + v = -16.30950643 + -15

Combine like terms: 15 + -15 = 0
0 + v = -16.30950643 + -15
v = -16.30950643 + -15

Combine like terms: -16.30950643 + -15 = -31.30950643
v = -31.30950643

Simplifying
v = -31.30950643


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.30950643, -31.30950643}

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