r^2-10r+11=0

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Solution for r^2-10r+11=0 equation: 


Simplifying
r2 + -10r + 11 = 0

Reorder the terms:
11 + -10r + r2 = 0

Solving
11 + -10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -10r + -11 + r2 = 0 + -11

Reorder the terms:
11 + -11 + -10r + r2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10r + r2 = 0 + -11
-10r + r2 = 0 + -11

Combine like terms: 0 + -11 = -11
-10r + r2 = -11

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 = -11 + 25

Reorder the terms:
25 + -10r + r2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + -10r + r2 = 14

Factor a perfect square on the left side:
(r + -5)(r + -5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(r + -5) equal to 3.741657387 and -3.741657387.


Subproblem 1
r + -5 = 3.741657387

Simplifying
r + -5 = 3.741657387

Reorder the terms:
-5 + r = 3.741657387

Solving
-5 + r = 3.741657387

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 = 3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + r = 3.741657387 + 5
r = 3.741657387 + 5

Combine like terms: 3.741657387 + 5 = 8.741657387
r = 8.741657387

Simplifying
r = 8.741657387


Subproblem 2
r + -5 = -3.741657387

Simplifying
r + -5 = -3.741657387

Reorder the terms:
-5 + r = -3.741657387

Solving
-5 + r = -3.741657387

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 = -3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + r = -3.741657387 + 5
r = -3.741657387 + 5

Combine like terms: -3.741657387 + 5 = 1.258342613
r = 1.258342613

Simplifying
r = 1.258342613


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.741657387, 1.258342613}

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