r^2-4r=30

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Solution for r^2-4r=30 equation: 


Simplifying
r2 + -4r = 30

Reorder the terms:
-4r + r2 = 30

Solving
-4r + r2 = 30

Solving for variable 'r'.

Reorder the terms:
-30 + -4r + r2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -4r + 30 + r2 = 0 + 30

Reorder the terms:
-30 + 30 + -4r + r2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -4r + r2 = 0 + 30
-4r + r2 = 0 + 30

Combine like terms: 0 + 30 = 30
-4r + r2 = 30

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 30 + 4

Reorder the terms:
4 + -4r + r2 = 30 + 4

Combine like terms: 30 + 4 = 34
4 + -4r + r2 = 34

Factor a perfect square on the left side:
(r + -2)(r + -2) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(r + -2) equal to 5.830951895 and -5.830951895.


Subproblem 1
r + -2 = 5.830951895

Simplifying
r + -2 = 5.830951895

Reorder the terms:
-2 + r = 5.830951895

Solving
-2 + r = 5.830951895

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = 5.830951895 + 2

Combine like terms: -2 + 2 = 0
0 + r = 5.830951895 + 2
r = 5.830951895 + 2

Combine like terms: 5.830951895 + 2 = 7.830951895
r = 7.830951895

Simplifying
r = 7.830951895


Subproblem 2
r + -2 = -5.830951895

Simplifying
r + -2 = -5.830951895

Reorder the terms:
-2 + r = -5.830951895

Solving
-2 + r = -5.830951895

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = -5.830951895 + 2

Combine like terms: -2 + 2 = 0
0 + r = -5.830951895 + 2
r = -5.830951895 + 2

Combine like terms: -5.830951895 + 2 = -3.830951895
r = -3.830951895

Simplifying
r = -3.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {7.830951895, -3.830951895}

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