(30+2x)(50+2x)=1326

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Solution for (30+2x)(50+2x)=1326 equation: 


Simplifying
(30 + 2x)(50 + 2x) = 1326

Multiply (30 + 2x) * (50 + 2x)
(30(50 + 2x) + 2x * (50 + 2x)) = 1326
((50 * 30 + 2x * 30) + 2x * (50 + 2x)) = 1326
((1500 + 60x) + 2x * (50 + 2x)) = 1326
(1500 + 60x + (50 * 2x + 2x * 2x)) = 1326
(1500 + 60x + (100x + 4x2)) = 1326

Combine like terms: 60x + 100x = 160x
(1500 + 160x + 4x2) = 1326

Solving
1500 + 160x + 4x2 = 1326

Solving for variable 'x'.

Reorder the terms:
1500 + -1326 + 160x + 4x2 = 1326 + -1326

Combine like terms: 1500 + -1326 = 174
174 + 160x + 4x2 = 1326 + -1326

Combine like terms: 1326 + -1326 = 0
174 + 160x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(87 + 80x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(87 + 80x + 2x2)' equal to zero and attempt to solve:

Simplifying
87 + 80x + 2x2 = 0

Solving
87 + 80x + 2x2 = 0

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

Divide each side by '2'.
43.5 + 40x + x2 = 0

Move the constant term to the right:

Add '-43.5' to each side of the equation.
43.5 + 40x + -43.5 + x2 = 0 + -43.5

Reorder the terms:
43.5 + -43.5 + 40x + x2 = 0 + -43.5

Combine like terms: 43.5 + -43.5 = 0.0
0.0 + 40x + x2 = 0 + -43.5
40x + x2 = 0 + -43.5

Combine like terms: 0 + -43.5 = -43.5
40x + x2 = -43.5

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = -43.5 + 400

Reorder the terms:
400 + 40x + x2 = -43.5 + 400

Combine like terms: -43.5 + 400 = 356.5
400 + 40x + x2 = 356.5

Factor a perfect square on the left side:
(x + 20)(x + 20) = 356.5

Calculate the square root of the right side: 18.881207588

Break this problem into two subproblems by setting 
(x + 20) equal to 18.881207588 and -18.881207588.


Subproblem 1
x + 20 = 18.881207588

Simplifying
x + 20 = 18.881207588

Reorder the terms:
20 + x = 18.881207588

Solving
20 + x = 18.881207588

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 18.881207588 + -20

Combine like terms: 20 + -20 = 0
0 + x = 18.881207588 + -20
x = 18.881207588 + -20

Combine like terms: 18.881207588 + -20 = -1.118792412
x = -1.118792412

Simplifying
x = -1.118792412


Subproblem 2
x + 20 = -18.881207588

Simplifying
x + 20 = -18.881207588

Reorder the terms:
20 + x = -18.881207588

Solving
20 + x = -18.881207588

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -18.881207588 + -20

Combine like terms: 20 + -20 = 0
0 + x = -18.881207588 + -20
x = -18.881207588 + -20

Combine like terms: -18.881207588 + -20 = -38.881207588
x = -38.881207588

Simplifying
x = -38.881207588


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.118792412, -38.881207588}
Solution
x = {-1.118792412, -38.881207588}

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