r^2-24r-47=0

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Solution for r^2-24r-47=0 equation: 


Simplifying
r2 + -24r + -47 = 0

Reorder the terms:
-47 + -24r + r2 = 0

Solving
-47 + -24r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -24r + 47 + r2 = 0 + 47

Reorder the terms:
-47 + 47 + -24r + r2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -24r + r2 = 0 + 47
-24r + r2 = 0 + 47

Combine like terms: 0 + 47 = 47
-24r + r2 = 47

The r term is -24r.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24r + 144 + r2 = 47 + 144

Reorder the terms:
144 + -24r + r2 = 47 + 144

Combine like terms: 47 + 144 = 191
144 + -24r + r2 = 191

Factor a perfect square on the left side:
(r + -12)(r + -12) = 191

Calculate the square root of the right side: 13.820274961

Break this problem into two subproblems by setting 
(r + -12) equal to 13.820274961 and -13.820274961.


Subproblem 1
r + -12 = 13.820274961

Simplifying
r + -12 = 13.820274961

Reorder the terms:
-12 + r = 13.820274961

Solving
-12 + r = 13.820274961

Solving for variable 'r'.

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

Add '12' to each side of the equation.
-12 + 12 + r = 13.820274961 + 12

Combine like terms: -12 + 12 = 0
0 + r = 13.820274961 + 12
r = 13.820274961 + 12

Combine like terms: 13.820274961 + 12 = 25.820274961
r = 25.820274961

Simplifying
r = 25.820274961


Subproblem 2
r + -12 = -13.820274961

Simplifying
r + -12 = -13.820274961

Reorder the terms:
-12 + r = -13.820274961

Solving
-12 + r = -13.820274961

Solving for variable 'r'.

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

Add '12' to each side of the equation.
-12 + 12 + r = -13.820274961 + 12

Combine like terms: -12 + 12 = 0
0 + r = -13.820274961 + 12
r = -13.820274961 + 12

Combine like terms: -13.820274961 + 12 = -1.820274961
r = -1.820274961

Simplifying
r = -1.820274961


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {25.820274961, -1.820274961}

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