v^2+28v+62=0

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Solution for v^2+28v+62=0 equation: 


Simplifying
v2 + 28v + 62 = 0

Reorder the terms:
62 + 28v + v2 = 0

Solving
62 + 28v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-62' to each side of the equation.
62 + 28v + -62 + v2 = 0 + -62

Reorder the terms:
62 + -62 + 28v + v2 = 0 + -62

Combine like terms: 62 + -62 = 0
0 + 28v + v2 = 0 + -62
28v + v2 = 0 + -62

Combine like terms: 0 + -62 = -62
28v + v2 = -62

The v term is 28v.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28v + 196 + v2 = -62 + 196

Reorder the terms:
196 + 28v + v2 = -62 + 196

Combine like terms: -62 + 196 = 134
196 + 28v + v2 = 134

Factor a perfect square on the left side:
(v + 14)(v + 14) = 134

Calculate the square root of the right side: 11.575836903

Break this problem into two subproblems by setting 
(v + 14) equal to 11.575836903 and -11.575836903.


Subproblem 1
v + 14 = 11.575836903

Simplifying
v + 14 = 11.575836903

Reorder the terms:
14 + v = 11.575836903

Solving
14 + v = 11.575836903

Solving for variable 'v'.

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

Add '-14' to each side of the equation.
14 + -14 + v = 11.575836903 + -14

Combine like terms: 14 + -14 = 0
0 + v = 11.575836903 + -14
v = 11.575836903 + -14

Combine like terms: 11.575836903 + -14 = -2.424163097
v = -2.424163097

Simplifying
v = -2.424163097


Subproblem 2
v + 14 = -11.575836903

Simplifying
v + 14 = -11.575836903

Reorder the terms:
14 + v = -11.575836903

Solving
14 + v = -11.575836903

Solving for variable 'v'.

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

Add '-14' to each side of the equation.
14 + -14 + v = -11.575836903 + -14

Combine like terms: 14 + -14 = 0
0 + v = -11.575836903 + -14
v = -11.575836903 + -14

Combine like terms: -11.575836903 + -14 = -25.575836903
v = -25.575836903

Simplifying
v = -25.575836903


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-2.424163097, -25.575836903}

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