r^2-10r+2=0

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


Simplifying
r2 + -10r + 2 = 0

Reorder the terms:
2 + -10r + r2 = 0

Solving
2 + -10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -10r + -2 + r2 = 0 + -2

Reorder the terms:
2 + -2 + -10r + r2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -10r + r2 = 0 + -2
-10r + r2 = 0 + -2

Combine like terms: 0 + -2 = -2
-10r + r2 = -2

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 = -2 + 25

Reorder the terms:
25 + -10r + r2 = -2 + 25

Combine like terms: -2 + 25 = 23
25 + -10r + r2 = 23

Factor a perfect square on the left side:
(r + -5)(r + -5) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(r + -5) equal to 4.795831523 and -4.795831523.


Subproblem 1
r + -5 = 4.795831523

Simplifying
r + -5 = 4.795831523

Reorder the terms:
-5 + r = 4.795831523

Solving
-5 + r = 4.795831523

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 = 4.795831523 + 5

Combine like terms: -5 + 5 = 0
0 + r = 4.795831523 + 5
r = 4.795831523 + 5

Combine like terms: 4.795831523 + 5 = 9.795831523
r = 9.795831523

Simplifying
r = 9.795831523


Subproblem 2
r + -5 = -4.795831523

Simplifying
r + -5 = -4.795831523

Reorder the terms:
-5 + r = -4.795831523

Solving
-5 + r = -4.795831523

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 = -4.795831523 + 5

Combine like terms: -5 + 5 = 0
0 + r = -4.795831523 + 5
r = -4.795831523 + 5

Combine like terms: -4.795831523 + 5 = 0.204168477
r = 0.204168477

Simplifying
r = 0.204168477


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.795831523, 0.204168477}

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