r^2+14r-11=0

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Solution for r^2+14r-11=0 equation: 


Simplifying
r2 + 14r + -11 = 0

Reorder the terms:
-11 + 14r + r2 = 0

Solving
-11 + 14r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 14r + 11 + r2 = 0 + 11

Reorder the terms:
-11 + 11 + 14r + r2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 14r + r2 = 0 + 11
14r + r2 = 0 + 11

Combine like terms: 0 + 11 = 11
14r + r2 = 11

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 = 11 + 49

Reorder the terms:
49 + 14r + r2 = 11 + 49

Combine like terms: 11 + 49 = 60
49 + 14r + r2 = 60

Factor a perfect square on the left side:
(r + 7)(r + 7) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(r + 7) equal to 7.745966692 and -7.745966692.


Subproblem 1
r + 7 = 7.745966692

Simplifying
r + 7 = 7.745966692

Reorder the terms:
7 + r = 7.745966692

Solving
7 + r = 7.745966692

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 = 7.745966692 + -7

Combine like terms: 7 + -7 = 0
0 + r = 7.745966692 + -7
r = 7.745966692 + -7

Combine like terms: 7.745966692 + -7 = 0.745966692
r = 0.745966692

Simplifying
r = 0.745966692


Subproblem 2
r + 7 = -7.745966692

Simplifying
r + 7 = -7.745966692

Reorder the terms:
7 + r = -7.745966692

Solving
7 + r = -7.745966692

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 = -7.745966692 + -7

Combine like terms: 7 + -7 = 0
0 + r = -7.745966692 + -7
r = -7.745966692 + -7

Combine like terms: -7.745966692 + -7 = -14.745966692
r = -14.745966692

Simplifying
r = -14.745966692


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.745966692, -14.745966692}

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