(12+2x)(24+2x)=252

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Solution for (12+2x)(24+2x)=252 equation: 


Simplifying
(12 + 2x)(24 + 2x) = 252

Multiply (12 + 2x) * (24 + 2x)
(12(24 + 2x) + 2x * (24 + 2x)) = 252
((24 * 12 + 2x * 12) + 2x * (24 + 2x)) = 252
((288 + 24x) + 2x * (24 + 2x)) = 252
(288 + 24x + (24 * 2x + 2x * 2x)) = 252
(288 + 24x + (48x + 4x2)) = 252

Combine like terms: 24x + 48x = 72x
(288 + 72x + 4x2) = 252

Solving
288 + 72x + 4x2 = 252

Solving for variable 'x'.

Reorder the terms:
288 + -252 + 72x + 4x2 = 252 + -252

Combine like terms: 288 + -252 = 36
36 + 72x + 4x2 = 252 + -252

Combine like terms: 252 + -252 = 0
36 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 18x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
9 + 18x + x2 = 0

Solving
9 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 18x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 18x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 18x + x2 = 0 + -9
18x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
18x + x2 = -9

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -9 + 81

Reorder the terms:
81 + 18x + x2 = -9 + 81

Combine like terms: -9 + 81 = 72
81 + 18x + x2 = 72

Factor a perfect square on the left side:
(x + 9)(x + 9) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + 9) equal to 8.485281374 and -8.485281374.


Subproblem 1
x + 9 = 8.485281374

Simplifying
x + 9 = 8.485281374

Reorder the terms:
9 + x = 8.485281374

Solving
9 + x = 8.485281374

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 8.485281374 + -9

Combine like terms: 9 + -9 = 0
0 + x = 8.485281374 + -9
x = 8.485281374 + -9

Combine like terms: 8.485281374 + -9 = -0.514718626
x = -0.514718626

Simplifying
x = -0.514718626


Subproblem 2
x + 9 = -8.485281374

Simplifying
x + 9 = -8.485281374

Reorder the terms:
9 + x = -8.485281374

Solving
9 + x = -8.485281374

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -8.485281374 + -9

Combine like terms: 9 + -9 = 0
0 + x = -8.485281374 + -9
x = -8.485281374 + -9

Combine like terms: -8.485281374 + -9 = -17.485281374
x = -17.485281374

Simplifying
x = -17.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.514718626, -17.485281374}
Solution
x = {-0.514718626, -17.485281374}

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