r^2-6r-18=0

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Solution for r^2-6r-18=0 equation: 


Simplifying
r2 + -6r + -18 = 0

Reorder the terms:
-18 + -6r + r2 = 0

Solving
-18 + -6r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -6r + 18 + r2 = 0 + 18

Reorder the terms:
-18 + 18 + -6r + r2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -6r + r2 = 0 + 18
-6r + r2 = 0 + 18

Combine like terms: 0 + 18 = 18
-6r + r2 = 18

The r term is -6r.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6r + 9 + r2 = 18 + 9

Reorder the terms:
9 + -6r + r2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + -6r + r2 = 27

Factor a perfect square on the left side:
(r + -3)(r + -3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(r + -3) equal to 5.196152423 and -5.196152423.


Subproblem 1
r + -3 = 5.196152423

Simplifying
r + -3 = 5.196152423

Reorder the terms:
-3 + r = 5.196152423

Solving
-3 + r = 5.196152423

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = 5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + r = 5.196152423 + 3
r = 5.196152423 + 3

Combine like terms: 5.196152423 + 3 = 8.196152423
r = 8.196152423

Simplifying
r = 8.196152423


Subproblem 2
r + -3 = -5.196152423

Simplifying
r + -3 = -5.196152423

Reorder the terms:
-3 + r = -5.196152423

Solving
-3 + r = -5.196152423

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + r = -5.196152423 + 3

Combine like terms: -3 + 3 = 0
0 + r = -5.196152423 + 3
r = -5.196152423 + 3

Combine like terms: -5.196152423 + 3 = -2.196152423
r = -2.196152423

Simplifying
r = -2.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.196152423, -2.196152423}

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