(20+2x)(20+2x)=600

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Solution for (20+2x)(20+2x)=600 equation: 


Simplifying
(20 + 2x)(20 + 2x) = 600

Multiply (20 + 2x) * (20 + 2x)
(20(20 + 2x) + 2x * (20 + 2x)) = 600
((20 * 20 + 2x * 20) + 2x * (20 + 2x)) = 600
((400 + 40x) + 2x * (20 + 2x)) = 600
(400 + 40x + (20 * 2x + 2x * 2x)) = 600
(400 + 40x + (40x + 4x2)) = 600

Combine like terms: 40x + 40x = 80x
(400 + 80x + 4x2) = 600

Solving
400 + 80x + 4x2 = 600

Solving for variable 'x'.

Reorder the terms:
400 + -600 + 80x + 4x2 = 600 + -600

Combine like terms: 400 + -600 = -200
-200 + 80x + 4x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-200 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + 20x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-50 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + 20x + x2 = 0

Solving
-50 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 20x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 20x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 20x + x2 = 0 + 50
20x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
20x + x2 = 50

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 50 + 100

Reorder the terms:
100 + 20x + x2 = 50 + 100

Combine like terms: 50 + 100 = 150
100 + 20x + x2 = 150

Factor a perfect square on the left side:
(x + 10)(x + 10) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(x + 10) equal to 12.247448714 and -12.247448714.


Subproblem 1
x + 10 = 12.247448714

Simplifying
x + 10 = 12.247448714

Reorder the terms:
10 + x = 12.247448714

Solving
10 + x = 12.247448714

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 12.247448714 + -10

Combine like terms: 10 + -10 = 0
0 + x = 12.247448714 + -10
x = 12.247448714 + -10

Combine like terms: 12.247448714 + -10 = 2.247448714
x = 2.247448714

Simplifying
x = 2.247448714


Subproblem 2
x + 10 = -12.247448714

Simplifying
x + 10 = -12.247448714

Reorder the terms:
10 + x = -12.247448714

Solving
10 + x = -12.247448714

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -12.247448714 + -10

Combine like terms: 10 + -10 = 0
0 + x = -12.247448714 + -10
x = -12.247448714 + -10

Combine like terms: -12.247448714 + -10 = -22.247448714
x = -22.247448714

Simplifying
x = -22.247448714


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.247448714, -22.247448714}
Solution
x = {2.247448714, -22.247448714}

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