20R=4(R*R+5)

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Solution for 20R=4(R*R+5) equation: 


Simplifying
20R = 4(R * R + 5)

Multiply R * R
20R = 4(R2 + 5)

Reorder the terms:
20R = 4(5 + R2)
20R = (5 * 4 + R2 * 4)
20R = (20 + 4R2)

Solving
20R = 20 + 4R2

Solving for variable 'R'.

Reorder the terms:
-20 + 20R + -4R2 = 20 + 4R2 + -20 + -4R2

Reorder the terms:
-20 + 20R + -4R2 = 20 + -20 + 4R2 + -4R2

Combine like terms: 20 + -20 = 0
-20 + 20R + -4R2 = 0 + 4R2 + -4R2
-20 + 20R + -4R2 = 4R2 + -4R2

Combine like terms: 4R2 + -4R2 = 0
-20 + 20R + -4R2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 5R + -1R2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + 5R + -1R2)' equal to zero and attempt to solve:

Simplifying
-5 + 5R + -1R2 = 0

Solving
-5 + 5R + -1R2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -5R + R2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5R + -5 + R2 = 0 + -5

Reorder the terms:
5 + -5 + -5R + R2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5R + R2 = 0 + -5
-5R + R2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5R + R2 = -5

The R term is -5R.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5R + 6.25 + R2 = -5 + 6.25

Reorder the terms:
6.25 + -5R + R2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + -5R + R2 = 1.25

Factor a perfect square on the left side:
(R + -2.5)(R + -2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(R + -2.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
R + -2.5 = 1.118033989

Simplifying
R + -2.5 = 1.118033989

Reorder the terms:
-2.5 + R = 1.118033989

Solving
-2.5 + R = 1.118033989

Solving for variable 'R'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + R = 1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + R = 1.118033989 + 2.5
R = 1.118033989 + 2.5

Combine like terms: 1.118033989 + 2.5 = 3.618033989
R = 3.618033989

Simplifying
R = 3.618033989


Subproblem 2
R + -2.5 = -1.118033989

Simplifying
R + -2.5 = -1.118033989

Reorder the terms:
-2.5 + R = -1.118033989

Solving
-2.5 + R = -1.118033989

Solving for variable 'R'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + R = -1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + R = -1.118033989 + 2.5
R = -1.118033989 + 2.5

Combine like terms: -1.118033989 + 2.5 = 1.381966011
R = 1.381966011

Simplifying
R = 1.381966011


Solution
The solution to the problem is based on the solutions
from the subproblems.
R = {3.618033989, 1.381966011}
Solution
R = {3.618033989, 1.381966011}

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