r^2+11r-66=0

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Solution for r^2+11r-66=0 equation: 


Simplifying
r2 + 11r + -66 = 0

Reorder the terms:
-66 + 11r + r2 = 0

Solving
-66 + 11r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 11r + 66 + r2 = 0 + 66

Reorder the terms:
-66 + 66 + 11r + r2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 11r + r2 = 0 + 66
11r + r2 = 0 + 66

Combine like terms: 0 + 66 = 66
11r + r2 = 66

The r term is 11r.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11r + 30.25 + r2 = 66 + 30.25

Reorder the terms:
30.25 + 11r + r2 = 66 + 30.25

Combine like terms: 66 + 30.25 = 96.25
30.25 + 11r + r2 = 96.25

Factor a perfect square on the left side:
(r + 5.5)(r + 5.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(r + 5.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
r + 5.5 = 9.810708435

Simplifying
r + 5.5 = 9.810708435

Reorder the terms:
5.5 + r = 9.810708435

Solving
5.5 + r = 9.810708435

Solving for variable 'r'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + r = 9.810708435 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + r = 9.810708435 + -5.5
r = 9.810708435 + -5.5

Combine like terms: 9.810708435 + -5.5 = 4.310708435
r = 4.310708435

Simplifying
r = 4.310708435


Subproblem 2
r + 5.5 = -9.810708435

Simplifying
r + 5.5 = -9.810708435

Reorder the terms:
5.5 + r = -9.810708435

Solving
5.5 + r = -9.810708435

Solving for variable 'r'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + r = -9.810708435 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + r = -9.810708435 + -5.5
r = -9.810708435 + -5.5

Combine like terms: -9.810708435 + -5.5 = -15.310708435
r = -15.310708435

Simplifying
r = -15.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.310708435, -15.310708435}

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