r^2-10r-50=0

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Solution for r^2-10r-50=0 equation: 


Simplifying
r2 + -10r + -50 = 0

Reorder the terms:
-50 + -10r + r2 = 0

Solving
-50 + -10r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -10r + 50 + r2 = 0 + 50

Reorder the terms:
-50 + 50 + -10r + r2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -10r + r2 = 0 + 50
-10r + r2 = 0 + 50

Combine like terms: 0 + 50 = 50
-10r + r2 = 50

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 = 50 + 25

Reorder the terms:
25 + -10r + r2 = 50 + 25

Combine like terms: 50 + 25 = 75
25 + -10r + r2 = 75

Factor a perfect square on the left side:
(r + -5)(r + -5) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(r + -5) equal to 8.660254038 and -8.660254038.


Subproblem 1
r + -5 = 8.660254038

Simplifying
r + -5 = 8.660254038

Reorder the terms:
-5 + r = 8.660254038

Solving
-5 + r = 8.660254038

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 = 8.660254038 + 5

Combine like terms: -5 + 5 = 0
0 + r = 8.660254038 + 5
r = 8.660254038 + 5

Combine like terms: 8.660254038 + 5 = 13.660254038
r = 13.660254038

Simplifying
r = 13.660254038


Subproblem 2
r + -5 = -8.660254038

Simplifying
r + -5 = -8.660254038

Reorder the terms:
-5 + r = -8.660254038

Solving
-5 + r = -8.660254038

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 = -8.660254038 + 5

Combine like terms: -5 + 5 = 0
0 + r = -8.660254038 + 5
r = -8.660254038 + 5

Combine like terms: -8.660254038 + 5 = -3.660254038
r = -3.660254038

Simplifying
r = -3.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {13.660254038, -3.660254038}

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