5(r-2)(r-2)=35

Solution for 5(r-2)(r-2)=35 equation:

Simplifying
5(r + -2)(r + -2) = 35

Reorder the terms:
5(-2 + r)(r + -2) = 35

Reorder the terms:
5(-2 + r)(-2 + r) = 35

Multiply (-2 + r) * (-2 + r)
5(-2(-2 + r) + r(-2 + r)) = 35
5((-2 * -2 + r * -2) + r(-2 + r)) = 35
5((4 + -2r) + r(-2 + r)) = 35
5(4 + -2r + (-2 * r + r * r)) = 35
5(4 + -2r + (-2r + r2)) = 35

Combine like terms: -2r + -2r = -4r
5(4 + -4r + r2) = 35
(4 * 5 + -4r * 5 + r2 * 5) = 35
(20 + -20r + 5r2) = 35

Solving
20 + -20r + 5r2 = 35

Solving for variable 'r'.

Reorder the terms:
20 + -35 + -20r + 5r2 = 35 + -35

Combine like terms: 20 + -35 = -15
-15 + -20r + 5r2 = 35 + -35

Combine like terms: 35 + -35 = 0
-15 + -20r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -4r + r2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + -4r + r2)' equal to zero and attempt to solve:

Simplifying
-3 + -4r + r2 = 0

Solving
-3 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4r + 3 + r2 = 0 + 3

Reorder the terms:
-3 + 3 + -4r + r2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4r + r2 = 0 + 3
-4r + r2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4r + r2 = 3

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 = 3 + 4

Reorder the terms:
4 + -4r + r2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4r + r2 = 7

Factor a perfect square on the left side:
(r + -2)(r + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(r + -2) equal to 2.645751311 and -2.645751311.

Subproblem 1
r + -2 = 2.645751311

Simplifying
r + -2 = 2.645751311

Reorder the terms:
-2 + r = 2.645751311

Solving
-2 + r = 2.645751311

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 = 2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + r = 2.645751311 + 2
r = 2.645751311 + 2

Combine like terms: 2.645751311 + 2 = 4.645751311
r = 4.645751311

Simplifying
r = 4.645751311

Subproblem 2
r + -2 = -2.645751311

Simplifying
r + -2 = -2.645751311

Reorder the terms:
-2 + r = -2.645751311

Solving
-2 + r = -2.645751311

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 = -2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + r = -2.645751311 + 2
r = -2.645751311 + 2

Combine like terms: -2.645751311 + 2 = -0.645751311
r = -0.645751311

Simplifying
r = -0.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.645751311, -0.645751311}
Solution
r = {4.645751311, -0.645751311}