r^2-3r=50

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Solution for r^2-3r=50 equation: 


Simplifying
r2 + -3r = 50

Reorder the terms:
-3r + r2 = 50

Solving
-3r + r2 = 50

Solving for variable 'r'.

Reorder the terms:
-50 + -3r + r2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + -3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -3r + 50 + r2 = 0 + 50

Reorder the terms:
-50 + 50 + -3r + r2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -3r + r2 = 0 + 50
-3r + r2 = 0 + 50

Combine like terms: 0 + 50 = 50
-3r + r2 = 50

The r term is -3r.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3r + 2.25 + r2 = 50 + 2.25

Reorder the terms:
2.25 + -3r + r2 = 50 + 2.25

Combine like terms: 50 + 2.25 = 52.25
2.25 + -3r + r2 = 52.25

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(r + -1.5) equal to 7.228416147 and -7.228416147.


Subproblem 1
r + -1.5 = 7.228416147

Simplifying
r + -1.5 = 7.228416147

Reorder the terms:
-1.5 + r = 7.228416147

Solving
-1.5 + r = 7.228416147

Solving for variable 'r'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + r = 7.228416147 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 7.228416147 + 1.5
r = 7.228416147 + 1.5

Combine like terms: 7.228416147 + 1.5 = 8.728416147
r = 8.728416147

Simplifying
r = 8.728416147


Subproblem 2
r + -1.5 = -7.228416147

Simplifying
r + -1.5 = -7.228416147

Reorder the terms:
-1.5 + r = -7.228416147

Solving
-1.5 + r = -7.228416147

Solving for variable 'r'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + r = -7.228416147 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -7.228416147 + 1.5
r = -7.228416147 + 1.5

Combine like terms: -7.228416147 + 1.5 = -5.728416147
r = -5.728416147

Simplifying
r = -5.728416147


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {8.728416147, -5.728416147}

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