(100+2x)(150+x)=18000

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Solution for (100+2x)(150+x)=18000 equation: 


Simplifying
(100 + 2x)(150 + x) = 18000

Multiply (100 + 2x) * (150 + x)
(100(150 + x) + 2x * (150 + x)) = 18000
((150 * 100 + x * 100) + 2x * (150 + x)) = 18000
((15000 + 100x) + 2x * (150 + x)) = 18000
(15000 + 100x + (150 * 2x + x * 2x)) = 18000
(15000 + 100x + (300x + 2x2)) = 18000

Combine like terms: 100x + 300x = 400x
(15000 + 400x + 2x2) = 18000

Solving
15000 + 400x + 2x2 = 18000

Solving for variable 'x'.

Reorder the terms:
15000 + -18000 + 400x + 2x2 = 18000 + -18000

Combine like terms: 15000 + -18000 = -3000
-3000 + 400x + 2x2 = 18000 + -18000

Combine like terms: 18000 + -18000 = 0
-3000 + 400x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1500 + 200x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1500 + 200x + x2)' equal to zero and attempt to solve:

Simplifying
-1500 + 200x + x2 = 0

Solving
-1500 + 200x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1500' to each side of the equation.
-1500 + 200x + 1500 + x2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + 200x + x2 = 0 + 1500

Combine like terms: -1500 + 1500 = 0
0 + 200x + x2 = 0 + 1500
200x + x2 = 0 + 1500

Combine like terms: 0 + 1500 = 1500
200x + x2 = 1500

The x term is 200x.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200x + 10000 + x2 = 1500 + 10000

Reorder the terms:
10000 + 200x + x2 = 1500 + 10000

Combine like terms: 1500 + 10000 = 11500
10000 + 200x + x2 = 11500

Factor a perfect square on the left side:
(x + 100)(x + 100) = 11500

Calculate the square root of the right side: 107.238052948

Break this problem into two subproblems by setting 
(x + 100) equal to 107.238052948 and -107.238052948.


Subproblem 1
x + 100 = 107.238052948

Simplifying
x + 100 = 107.238052948

Reorder the terms:
100 + x = 107.238052948

Solving
100 + x = 107.238052948

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = 107.238052948 + -100

Combine like terms: 100 + -100 = 0
0 + x = 107.238052948 + -100
x = 107.238052948 + -100

Combine like terms: 107.238052948 + -100 = 7.238052948
x = 7.238052948

Simplifying
x = 7.238052948


Subproblem 2
x + 100 = -107.238052948

Simplifying
x + 100 = -107.238052948

Reorder the terms:
100 + x = -107.238052948

Solving
100 + x = -107.238052948

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = -107.238052948 + -100

Combine like terms: 100 + -100 = 0
0 + x = -107.238052948 + -100
x = -107.238052948 + -100

Combine like terms: -107.238052948 + -100 = -207.238052948
x = -207.238052948

Simplifying
x = -207.238052948


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.238052948, -207.238052948}
Solution
x = {7.238052948, -207.238052948}

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