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

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


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

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

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

Multiply (-5 + r) * (-5 + r)
5(-5(-5 + r) + r(-5 + r)) = 35
5((-5 * -5 + r * -5) + r(-5 + r)) = 35
5((25 + -5r) + r(-5 + r)) = 35
5(25 + -5r + (-5 * r + r * r)) = 35
5(25 + -5r + (-5r + r2)) = 35

Combine like terms: -5r + -5r = -10r
5(25 + -10r + r2) = 35
(25 * 5 + -10r * 5 + r2 * 5) = 35
(125 + -50r + 5r2) = 35

Solving
125 + -50r + 5r2 = 35

Solving for variable 'r'.

Reorder the terms:
125 + -35 + -50r + 5r2 = 35 + -35

Combine like terms: 125 + -35 = 90
90 + -50r + 5r2 = 35 + -35

Combine like terms: 35 + -35 = 0
90 + -50r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + -10r + r2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(18 + -10r + r2)' equal to zero and attempt to solve:

Simplifying
18 + -10r + r2 = 0

Solving
18 + -10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10r + -18 + r2 = 0 + -18

Reorder the terms:
18 + -18 + -10r + r2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10r + r2 = 0 + -18
-10r + r2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10r + r2 = -18

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 = -18 + 25

Reorder the terms:
25 + -10r + r2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + -10r + r2 = 7

Factor a perfect square on the left side:
(r + -5)(r + -5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(r + -5) equal to 2.645751311 and -2.645751311.


Subproblem 1
r + -5 = 2.645751311

Simplifying
r + -5 = 2.645751311

Reorder the terms:
-5 + r = 2.645751311

Solving
-5 + r = 2.645751311

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 = 2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + r = 2.645751311 + 5
r = 2.645751311 + 5

Combine like terms: 2.645751311 + 5 = 7.645751311
r = 7.645751311

Simplifying
r = 7.645751311


Subproblem 2
r + -5 = -2.645751311

Simplifying
r + -5 = -2.645751311

Reorder the terms:
-5 + r = -2.645751311

Solving
-5 + r = -2.645751311

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 = -2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + r = -2.645751311 + 5
r = -2.645751311 + 5

Combine like terms: -2.645751311 + 5 = 2.354248689
r = 2.354248689

Simplifying
r = 2.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {7.645751311, 2.354248689}
Solution
r = {7.645751311, 2.354248689}

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