(40+2x)(20+2x)=1200

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Solution for (40+2x)(20+2x)=1200 equation: 


Simplifying
(40 + 2x)(20 + 2x) = 1200

Multiply (40 + 2x) * (20 + 2x)
(40(20 + 2x) + 2x * (20 + 2x)) = 1200
((20 * 40 + 2x * 40) + 2x * (20 + 2x)) = 1200
((800 + 80x) + 2x * (20 + 2x)) = 1200
(800 + 80x + (20 * 2x + 2x * 2x)) = 1200
(800 + 80x + (40x + 4x2)) = 1200

Combine like terms: 80x + 40x = 120x
(800 + 120x + 4x2) = 1200

Solving
800 + 120x + 4x2 = 1200

Solving for variable 'x'.

Reorder the terms:
800 + -1200 + 120x + 4x2 = 1200 + -1200

Combine like terms: 800 + -1200 = -400
-400 + 120x + 4x2 = 1200 + -1200

Combine like terms: 1200 + -1200 = 0
-400 + 120x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-100 + 30x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-100 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + 30x + x2 = 0

Solving
-100 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 30x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 30x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 30x + x2 = 0 + 100
30x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
30x + x2 = 100

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

Add '225' to each side of the equation.
30x + 225 + x2 = 100 + 225

Reorder the terms:
225 + 30x + x2 = 100 + 225

Combine like terms: 100 + 225 = 325
225 + 30x + x2 = 325

Factor a perfect square on the left side:
(x + 15)(x + 15) = 325

Calculate the square root of the right side: 18.027756377

Break this problem into two subproblems by setting 
(x + 15) equal to 18.027756377 and -18.027756377.


Subproblem 1
x + 15 = 18.027756377

Simplifying
x + 15 = 18.027756377

Reorder the terms:
15 + x = 18.027756377

Solving
15 + x = 18.027756377

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 18.027756377 + -15

Combine like terms: 15 + -15 = 0
0 + x = 18.027756377 + -15
x = 18.027756377 + -15

Combine like terms: 18.027756377 + -15 = 3.027756377
x = 3.027756377

Simplifying
x = 3.027756377


Subproblem 2
x + 15 = -18.027756377

Simplifying
x + 15 = -18.027756377

Reorder the terms:
15 + x = -18.027756377

Solving
15 + x = -18.027756377

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -18.027756377 + -15

Combine like terms: 15 + -15 = 0
0 + x = -18.027756377 + -15
x = -18.027756377 + -15

Combine like terms: -18.027756377 + -15 = -33.027756377
x = -33.027756377

Simplifying
x = -33.027756377


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.027756377, -33.027756377}
Solution
x = {3.027756377, -33.027756377}

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