r^2-30r+220=0

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Solution for r^2-30r+220=0 equation: 


Simplifying
r2 + -30r + 220 = 0

Reorder the terms:
220 + -30r + r2 = 0

Solving
220 + -30r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-220' to each side of the equation.
220 + -30r + -220 + r2 = 0 + -220

Reorder the terms:
220 + -220 + -30r + r2 = 0 + -220

Combine like terms: 220 + -220 = 0
0 + -30r + r2 = 0 + -220
-30r + r2 = 0 + -220

Combine like terms: 0 + -220 = -220
-30r + r2 = -220

The r term is -30r.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30r + 225 + r2 = -220 + 225

Reorder the terms:
225 + -30r + r2 = -220 + 225

Combine like terms: -220 + 225 = 5
225 + -30r + r2 = 5

Factor a perfect square on the left side:
(r + -15)(r + -15) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(r + -15) equal to 2.236067978 and -2.236067978.


Subproblem 1
r + -15 = 2.236067978

Simplifying
r + -15 = 2.236067978

Reorder the terms:
-15 + r = 2.236067978

Solving
-15 + r = 2.236067978

Solving for variable 'r'.

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

Add '15' to each side of the equation.
-15 + 15 + r = 2.236067978 + 15

Combine like terms: -15 + 15 = 0
0 + r = 2.236067978 + 15
r = 2.236067978 + 15

Combine like terms: 2.236067978 + 15 = 17.236067978
r = 17.236067978

Simplifying
r = 17.236067978


Subproblem 2
r + -15 = -2.236067978

Simplifying
r + -15 = -2.236067978

Reorder the terms:
-15 + r = -2.236067978

Solving
-15 + r = -2.236067978

Solving for variable 'r'.

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

Add '15' to each side of the equation.
-15 + 15 + r = -2.236067978 + 15

Combine like terms: -15 + 15 = 0
0 + r = -2.236067978 + 15
r = -2.236067978 + 15

Combine like terms: -2.236067978 + 15 = 12.763932022
r = 12.763932022

Simplifying
r = 12.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {17.236067978, 12.763932022}

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