r^2-20r+52=0

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Solution for r^2-20r+52=0 equation: 


Simplifying
r2 + -20r + 52 = 0

Reorder the terms:
52 + -20r + r2 = 0

Solving
52 + -20r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + -20r + -52 + r2 = 0 + -52

Reorder the terms:
52 + -52 + -20r + r2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -20r + r2 = 0 + -52
-20r + r2 = 0 + -52

Combine like terms: 0 + -52 = -52
-20r + r2 = -52

The r term is -20r.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20r + 100 + r2 = -52 + 100

Reorder the terms:
100 + -20r + r2 = -52 + 100

Combine like terms: -52 + 100 = 48
100 + -20r + r2 = 48

Factor a perfect square on the left side:
(r + -10)(r + -10) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(r + -10) equal to 6.92820323 and -6.92820323.


Subproblem 1
r + -10 = 6.92820323

Simplifying
r + -10 = 6.92820323

Reorder the terms:
-10 + r = 6.92820323

Solving
-10 + r = 6.92820323

Solving for variable 'r'.

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

Add '10' to each side of the equation.
-10 + 10 + r = 6.92820323 + 10

Combine like terms: -10 + 10 = 0
0 + r = 6.92820323 + 10
r = 6.92820323 + 10

Combine like terms: 6.92820323 + 10 = 16.92820323
r = 16.92820323

Simplifying
r = 16.92820323


Subproblem 2
r + -10 = -6.92820323

Simplifying
r + -10 = -6.92820323

Reorder the terms:
-10 + r = -6.92820323

Solving
-10 + r = -6.92820323

Solving for variable 'r'.

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

Add '10' to each side of the equation.
-10 + 10 + r = -6.92820323 + 10

Combine like terms: -10 + 10 = 0
0 + r = -6.92820323 + 10
r = -6.92820323 + 10

Combine like terms: -6.92820323 + 10 = 3.07179677
r = 3.07179677

Simplifying
r = 3.07179677


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {16.92820323, 3.07179677}

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