r^2-18r+15=0

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Solution for r^2-18r+15=0 equation: 


Simplifying
r2 + -18r + 15 = 0

Reorder the terms:
15 + -18r + r2 = 0

Solving
15 + -18r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -18r + -15 + r2 = 0 + -15

Reorder the terms:
15 + -15 + -18r + r2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -18r + r2 = 0 + -15
-18r + r2 = 0 + -15

Combine like terms: 0 + -15 = -15
-18r + r2 = -15

The r term is -18r.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18r + 81 + r2 = -15 + 81

Reorder the terms:
81 + -18r + r2 = -15 + 81

Combine like terms: -15 + 81 = 66
81 + -18r + r2 = 66

Factor a perfect square on the left side:
(r + -9)(r + -9) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(r + -9) equal to 8.124038405 and -8.124038405.


Subproblem 1
r + -9 = 8.124038405

Simplifying
r + -9 = 8.124038405

Reorder the terms:
-9 + r = 8.124038405

Solving
-9 + r = 8.124038405

Solving for variable 'r'.

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

Add '9' to each side of the equation.
-9 + 9 + r = 8.124038405 + 9

Combine like terms: -9 + 9 = 0
0 + r = 8.124038405 + 9
r = 8.124038405 + 9

Combine like terms: 8.124038405 + 9 = 17.124038405
r = 17.124038405

Simplifying
r = 17.124038405


Subproblem 2
r + -9 = -8.124038405

Simplifying
r + -9 = -8.124038405

Reorder the terms:
-9 + r = -8.124038405

Solving
-9 + r = -8.124038405

Solving for variable 'r'.

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

Add '9' to each side of the equation.
-9 + 9 + r = -8.124038405 + 9

Combine like terms: -9 + 9 = 0
0 + r = -8.124038405 + 9
r = -8.124038405 + 9

Combine like terms: -8.124038405 + 9 = 0.875961595
r = 0.875961595

Simplifying
r = 0.875961595


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {17.124038405, 0.875961595}

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