(20+2x)(10+2x)=400

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Solution for (20+2x)(10+2x)=400 equation: 


Simplifying
(20 + 2x)(10 + 2x) = 400

Multiply (20 + 2x) * (10 + 2x)
(20(10 + 2x) + 2x * (10 + 2x)) = 400
((10 * 20 + 2x * 20) + 2x * (10 + 2x)) = 400
((200 + 40x) + 2x * (10 + 2x)) = 400
(200 + 40x + (10 * 2x + 2x * 2x)) = 400
(200 + 40x + (20x + 4x2)) = 400

Combine like terms: 40x + 20x = 60x
(200 + 60x + 4x2) = 400

Solving
200 + 60x + 4x2 = 400

Solving for variable 'x'.

Reorder the terms:
200 + -400 + 60x + 4x2 = 400 + -400

Combine like terms: 200 + -400 = -200
-200 + 60x + 4x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-200 + 60x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + 15x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-50 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + 15x + x2 = 0

Solving
-50 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 15x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 15x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 15x + x2 = 0 + 50
15x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
15x + x2 = 50

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 50 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 50 + 56.25

Combine like terms: 50 + 56.25 = 106.25
56.25 + 15x + x2 = 106.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(x + 7.5) equal to 10.307764064 and -10.307764064.


Subproblem 1
x + 7.5 = 10.307764064

Simplifying
x + 7.5 = 10.307764064

Reorder the terms:
7.5 + x = 10.307764064

Solving
7.5 + x = 10.307764064

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 10.307764064 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 10.307764064 + -7.5
x = 10.307764064 + -7.5

Combine like terms: 10.307764064 + -7.5 = 2.807764064
x = 2.807764064

Simplifying
x = 2.807764064


Subproblem 2
x + 7.5 = -10.307764064

Simplifying
x + 7.5 = -10.307764064

Reorder the terms:
7.5 + x = -10.307764064

Solving
7.5 + x = -10.307764064

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -10.307764064 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -10.307764064 + -7.5
x = -10.307764064 + -7.5

Combine like terms: -10.307764064 + -7.5 = -17.807764064
x = -17.807764064

Simplifying
x = -17.807764064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.807764064, -17.807764064}
Solution
x = {2.807764064, -17.807764064}

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