r^2-20r-243=0

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Solution for r^2-20r-243=0 equation: 


Simplifying
r2 + -20r + -243 = 0

Reorder the terms:
-243 + -20r + r2 = 0

Solving
-243 + -20r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '243' to each side of the equation.
-243 + -20r + 243 + r2 = 0 + 243

Reorder the terms:
-243 + 243 + -20r + r2 = 0 + 243

Combine like terms: -243 + 243 = 0
0 + -20r + r2 = 0 + 243
-20r + r2 = 0 + 243

Combine like terms: 0 + 243 = 243
-20r + r2 = 243

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 = 243 + 100

Reorder the terms:
100 + -20r + r2 = 243 + 100

Combine like terms: 243 + 100 = 343
100 + -20r + r2 = 343

Factor a perfect square on the left side:
(r + -10)(r + -10) = 343

Calculate the square root of the right side: 18.520259177

Break this problem into two subproblems by setting 
(r + -10) equal to 18.520259177 and -18.520259177.


Subproblem 1
r + -10 = 18.520259177

Simplifying
r + -10 = 18.520259177

Reorder the terms:
-10 + r = 18.520259177

Solving
-10 + r = 18.520259177

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 = 18.520259177 + 10

Combine like terms: -10 + 10 = 0
0 + r = 18.520259177 + 10
r = 18.520259177 + 10

Combine like terms: 18.520259177 + 10 = 28.520259177
r = 28.520259177

Simplifying
r = 28.520259177


Subproblem 2
r + -10 = -18.520259177

Simplifying
r + -10 = -18.520259177

Reorder the terms:
-10 + r = -18.520259177

Solving
-10 + r = -18.520259177

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 = -18.520259177 + 10

Combine like terms: -10 + 10 = 0
0 + r = -18.520259177 + 10
r = -18.520259177 + 10

Combine like terms: -18.520259177 + 10 = -8.520259177
r = -8.520259177

Simplifying
r = -8.520259177


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {28.520259177, -8.520259177}

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