r^2-10r+17=0

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Solution for r^2-10r+17=0 equation: 


Simplifying
r2 + -10r + 17 = 0

Reorder the terms:
17 + -10r + r2 = 0

Solving
17 + -10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -10r + -17 + r2 = 0 + -17

Reorder the terms:
17 + -17 + -10r + r2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -10r + r2 = 0 + -17
-10r + r2 = 0 + -17

Combine like terms: 0 + -17 = -17
-10r + r2 = -17

The r term is -10r.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r + 25 + r2 = -17 + 25

Reorder the terms:
25 + -10r + r2 = -17 + 25

Combine like terms: -17 + 25 = 8
25 + -10r + r2 = 8

Factor a perfect square on the left side:
(r + -5)(r + -5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(r + -5) equal to 2.828427125 and -2.828427125.


Subproblem 1
r + -5 = 2.828427125

Simplifying
r + -5 = 2.828427125

Reorder the terms:
-5 + r = 2.828427125

Solving
-5 + r = 2.828427125

Solving for variable 'r'.

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

Add '5' to each side of the equation.
-5 + 5 + r = 2.828427125 + 5

Combine like terms: -5 + 5 = 0
0 + r = 2.828427125 + 5
r = 2.828427125 + 5

Combine like terms: 2.828427125 + 5 = 7.828427125
r = 7.828427125

Simplifying
r = 7.828427125


Subproblem 2
r + -5 = -2.828427125

Simplifying
r + -5 = -2.828427125

Reorder the terms:
-5 + r = -2.828427125

Solving
-5 + r = -2.828427125

Solving for variable 'r'.

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

Add '5' to each side of the equation.
-5 + 5 + r = -2.828427125 + 5

Combine like terms: -5 + 5 = 0
0 + r = -2.828427125 + 5
r = -2.828427125 + 5

Combine like terms: -2.828427125 + 5 = 2.171572875
r = 2.171572875

Simplifying
r = 2.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {7.828427125, 2.171572875}

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