(15+2x)(20+2x)=600

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Solution for (15+2x)(20+2x)=600 equation: 


Simplifying
(15 + 2x)(20 + 2x) = 600

Multiply (15 + 2x) * (20 + 2x)
(15(20 + 2x) + 2x * (20 + 2x)) = 600
((20 * 15 + 2x * 15) + 2x * (20 + 2x)) = 600
((300 + 30x) + 2x * (20 + 2x)) = 600
(300 + 30x + (20 * 2x + 2x * 2x)) = 600
(300 + 30x + (40x + 4x2)) = 600

Combine like terms: 30x + 40x = 70x
(300 + 70x + 4x2) = 600

Solving
300 + 70x + 4x2 = 600

Solving for variable 'x'.

Reorder the terms:
300 + -600 + 70x + 4x2 = 600 + -600

Combine like terms: 300 + -600 = -300
-300 + 70x + 4x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-300 + 70x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-150 + 35x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-150 + 35x + 2x2)' equal to zero and attempt to solve:

Simplifying
-150 + 35x + 2x2 = 0

Solving
-150 + 35x + 2x2 = 0

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

Divide each side by '2'.
-75 + 17.5x + x2 = 0

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 17.5x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 17.5x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 17.5x + x2 = 0 + 75
17.5x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
17.5x + x2 = 75

The x term is 17.5x.  Take half its coefficient (8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
17.5x + 76.5625 + x2 = 75 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = 75 + 76.5625

Combine like terms: 75 + 76.5625 = 151.5625
76.5625 + 17.5x + x2 = 151.5625

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 151.5625

Calculate the square root of the right side: 12.311072252

Break this problem into two subproblems by setting 
(x + 8.75) equal to 12.311072252 and -12.311072252.


Subproblem 1
x + 8.75 = 12.311072252

Simplifying
x + 8.75 = 12.311072252

Reorder the terms:
8.75 + x = 12.311072252

Solving
8.75 + x = 12.311072252

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = 12.311072252 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = 12.311072252 + -8.75
x = 12.311072252 + -8.75

Combine like terms: 12.311072252 + -8.75 = 3.561072252
x = 3.561072252

Simplifying
x = 3.561072252


Subproblem 2
x + 8.75 = -12.311072252

Simplifying
x + 8.75 = -12.311072252

Reorder the terms:
8.75 + x = -12.311072252

Solving
8.75 + x = -12.311072252

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = -12.311072252 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = -12.311072252 + -8.75
x = -12.311072252 + -8.75

Combine like terms: -12.311072252 + -8.75 = -21.061072252
x = -21.061072252

Simplifying
x = -21.061072252


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.561072252, -21.061072252}
Solution
x = {3.561072252, -21.061072252}

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