(24+2x)(30+2x)=660

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Solution for (24+2x)(30+2x)=660 equation: 


Simplifying
(24 + 2x)(30 + 2x) = 660

Multiply (24 + 2x) * (30 + 2x)
(24(30 + 2x) + 2x * (30 + 2x)) = 660
((30 * 24 + 2x * 24) + 2x * (30 + 2x)) = 660
((720 + 48x) + 2x * (30 + 2x)) = 660
(720 + 48x + (30 * 2x + 2x * 2x)) = 660
(720 + 48x + (60x + 4x2)) = 660

Combine like terms: 48x + 60x = 108x
(720 + 108x + 4x2) = 660

Solving
720 + 108x + 4x2 = 660

Solving for variable 'x'.

Reorder the terms:
720 + -660 + 108x + 4x2 = 660 + -660

Combine like terms: 720 + -660 = 60
60 + 108x + 4x2 = 660 + -660

Combine like terms: 660 + -660 = 0
60 + 108x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 27x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(15 + 27x + x2)' equal to zero and attempt to solve:

Simplifying
15 + 27x + x2 = 0

Solving
15 + 27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 27x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 27x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 27x + x2 = 0 + -15
27x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
27x + x2 = -15

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = -15 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -15 + 182.25

Combine like terms: -15 + 182.25 = 167.25
182.25 + 27x + x2 = 167.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 167.25

Calculate the square root of the right side: 12.932517156

Break this problem into two subproblems by setting 
(x + 13.5) equal to 12.932517156 and -12.932517156.


Subproblem 1
x + 13.5 = 12.932517156

Simplifying
x + 13.5 = 12.932517156

Reorder the terms:
13.5 + x = 12.932517156

Solving
13.5 + x = 12.932517156

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 12.932517156 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 12.932517156 + -13.5
x = 12.932517156 + -13.5

Combine like terms: 12.932517156 + -13.5 = -0.567482844
x = -0.567482844

Simplifying
x = -0.567482844


Subproblem 2
x + 13.5 = -12.932517156

Simplifying
x + 13.5 = -12.932517156

Reorder the terms:
13.5 + x = -12.932517156

Solving
13.5 + x = -12.932517156

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -12.932517156 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -12.932517156 + -13.5
x = -12.932517156 + -13.5

Combine like terms: -12.932517156 + -13.5 = -26.432517156
x = -26.432517156

Simplifying
x = -26.432517156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.567482844, -26.432517156}
Solution
x = {-0.567482844, -26.432517156}

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