(50+2x)(20+2x)=5000

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Solution for (50+2x)(20+2x)=5000 equation: 


Simplifying
(50 + 2x)(20 + 2x) = 5000

Multiply (50 + 2x) * (20 + 2x)
(50(20 + 2x) + 2x * (20 + 2x)) = 5000
((20 * 50 + 2x * 50) + 2x * (20 + 2x)) = 5000
((1000 + 100x) + 2x * (20 + 2x)) = 5000
(1000 + 100x + (20 * 2x + 2x * 2x)) = 5000
(1000 + 100x + (40x + 4x2)) = 5000

Combine like terms: 100x + 40x = 140x
(1000 + 140x + 4x2) = 5000

Solving
1000 + 140x + 4x2 = 5000

Solving for variable 'x'.

Reorder the terms:
1000 + -5000 + 140x + 4x2 = 5000 + -5000

Combine like terms: 1000 + -5000 = -4000
-4000 + 140x + 4x2 = 5000 + -5000

Combine like terms: 5000 + -5000 = 0
-4000 + 140x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1000 + 35x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1000 + 35x + x2)' equal to zero and attempt to solve:

Simplifying
-1000 + 35x + x2 = 0

Solving
-1000 + 35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 35x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 35x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 35x + x2 = 0 + 1000
35x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
35x + x2 = 1000

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 1000 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 1000 + 306.25

Combine like terms: 1000 + 306.25 = 1306.25
306.25 + 35x + x2 = 1306.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 1306.25

Calculate the square root of the right side: 36.142080737

Break this problem into two subproblems by setting 
(x + 17.5) equal to 36.142080737 and -36.142080737.


Subproblem 1
x + 17.5 = 36.142080737

Simplifying
x + 17.5 = 36.142080737

Reorder the terms:
17.5 + x = 36.142080737

Solving
17.5 + x = 36.142080737

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 36.142080737 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 36.142080737 + -17.5
x = 36.142080737 + -17.5

Combine like terms: 36.142080737 + -17.5 = 18.642080737
x = 18.642080737

Simplifying
x = 18.642080737


Subproblem 2
x + 17.5 = -36.142080737

Simplifying
x + 17.5 = -36.142080737

Reorder the terms:
17.5 + x = -36.142080737

Solving
17.5 + x = -36.142080737

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -36.142080737 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -36.142080737 + -17.5
x = -36.142080737 + -17.5

Combine like terms: -36.142080737 + -17.5 = -53.642080737
x = -53.642080737

Simplifying
x = -53.642080737


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.642080737, -53.642080737}
Solution
x = {18.642080737, -53.642080737}

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