(10+2x)*(24+2x)=336

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Solution for (10+2x)*(24+2x)=336 equation: 


Simplifying
(10 + 2x)(24 + 2x) = 336

Multiply (10 + 2x) * (24 + 2x)
(10(24 + 2x) + 2x * (24 + 2x)) = 336
((24 * 10 + 2x * 10) + 2x * (24 + 2x)) = 336
((240 + 20x) + 2x * (24 + 2x)) = 336
(240 + 20x + (24 * 2x + 2x * 2x)) = 336
(240 + 20x + (48x + 4x2)) = 336

Combine like terms: 20x + 48x = 68x
(240 + 68x + 4x2) = 336

Solving
240 + 68x + 4x2 = 336

Solving for variable 'x'.

Reorder the terms:
240 + -336 + 68x + 4x2 = 336 + -336

Combine like terms: 240 + -336 = -96
-96 + 68x + 4x2 = 336 + -336

Combine like terms: 336 + -336 = 0
-96 + 68x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + 17x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-24 + 17x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 17x + x2 = 0

Solving
-24 + 17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 17x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 17x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 17x + x2 = 0 + 24
17x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
17x + x2 = 24

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 24 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 24 + 72.25

Combine like terms: 24 + 72.25 = 96.25
72.25 + 17x + x2 = 96.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 8.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
x + 8.5 = 9.810708435

Simplifying
x + 8.5 = 9.810708435

Reorder the terms:
8.5 + x = 9.810708435

Solving
8.5 + x = 9.810708435

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 9.810708435 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 9.810708435 + -8.5
x = 9.810708435 + -8.5

Combine like terms: 9.810708435 + -8.5 = 1.310708435
x = 1.310708435

Simplifying
x = 1.310708435


Subproblem 2
x + 8.5 = -9.810708435

Simplifying
x + 8.5 = -9.810708435

Reorder the terms:
8.5 + x = -9.810708435

Solving
8.5 + x = -9.810708435

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -9.810708435 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -9.810708435 + -8.5
x = -9.810708435 + -8.5

Combine like terms: -9.810708435 + -8.5 = -18.310708435
x = -18.310708435

Simplifying
x = -18.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.310708435, -18.310708435}
Solution
x = {1.310708435, -18.310708435}

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