v^2+14v-60=0

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Solution for v^2+14v-60=0 equation: 


Simplifying
v2 + 14v + -60 = 0

Reorder the terms:
-60 + 14v + v2 = 0

Solving
-60 + 14v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 14v + 60 + v2 = 0 + 60

Reorder the terms:
-60 + 60 + 14v + v2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 14v + v2 = 0 + 60
14v + v2 = 0 + 60

Combine like terms: 0 + 60 = 60
14v + v2 = 60

The v term is 14v.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14v + 49 + v2 = 60 + 49

Reorder the terms:
49 + 14v + v2 = 60 + 49

Combine like terms: 60 + 49 = 109
49 + 14v + v2 = 109

Factor a perfect square on the left side:
(v + 7)(v + 7) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(v + 7) equal to 10.440306509 and -10.440306509.


Subproblem 1
v + 7 = 10.440306509

Simplifying
v + 7 = 10.440306509

Reorder the terms:
7 + v = 10.440306509

Solving
7 + v = 10.440306509

Solving for variable 'v'.

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

Add '-7' to each side of the equation.
7 + -7 + v = 10.440306509 + -7

Combine like terms: 7 + -7 = 0
0 + v = 10.440306509 + -7
v = 10.440306509 + -7

Combine like terms: 10.440306509 + -7 = 3.440306509
v = 3.440306509

Simplifying
v = 3.440306509


Subproblem 2
v + 7 = -10.440306509

Simplifying
v + 7 = -10.440306509

Reorder the terms:
7 + v = -10.440306509

Solving
7 + v = -10.440306509

Solving for variable 'v'.

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

Add '-7' to each side of the equation.
7 + -7 + v = -10.440306509 + -7

Combine like terms: 7 + -7 = 0
0 + v = -10.440306509 + -7
v = -10.440306509 + -7

Combine like terms: -10.440306509 + -7 = -17.440306509
v = -17.440306509

Simplifying
v = -17.440306509


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.440306509, -17.440306509}

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