r^2+14r-1=0

Solution for r^2+14r-1=0 equation:

Simplifying
r2 + 14r + -1 = 0

Reorder the terms:
-1 + 14r + r2 = 0

Solving
-1 + 14r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 14r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + 14r + r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 14r + r2 = 0 + 1
14r + r2 = 0 + 1

Combine like terms: 0 + 1 = 1
14r + r2 = 1

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

Add '49' to each side of the equation.
14r + 49 + r2 = 1 + 49

Reorder the terms:
49 + 14r + r2 = 1 + 49

Combine like terms: 1 + 49 = 50
49 + 14r + r2 = 50

Factor a perfect square on the left side:
(r + 7)(r + 7) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(r + 7) equal to 7.071067812 and -7.071067812.

Subproblem 1
r + 7 = 7.071067812

Simplifying
r + 7 = 7.071067812

Reorder the terms:
7 + r = 7.071067812

Solving
7 + r = 7.071067812

Solving for variable 'r'.

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

Add '-7' to each side of the equation.
7 + -7 + r = 7.071067812 + -7

Combine like terms: 7 + -7 = 0
0 + r = 7.071067812 + -7
r = 7.071067812 + -7

Combine like terms: 7.071067812 + -7 = 0.071067812
r = 0.071067812

Simplifying
r = 0.071067812

Subproblem 2
r + 7 = -7.071067812

Simplifying
r + 7 = -7.071067812

Reorder the terms:
7 + r = -7.071067812

Solving
7 + r = -7.071067812

Solving for variable 'r'.

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

Add '-7' to each side of the equation.
7 + -7 + r = -7.071067812 + -7

Combine like terms: 7 + -7 = 0
0 + r = -7.071067812 + -7
r = -7.071067812 + -7

Combine like terms: -7.071067812 + -7 = -14.071067812
r = -14.071067812

Simplifying
r = -14.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.071067812, -14.071067812}