(17+2x)(13*2x)=396

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Solution for (17+2x)(13*2x)=396 equation:


Simplifying
(17 + 2x)(13 * 2x) = 396

Multiply 13 * 2
(17 + 2x)(26x) = 396

Remove parenthesis around (26x)
(17 + 2x) * 26x = 396

Reorder the terms for easier multiplication:
26x(17 + 2x) = 396
(17 * 26x + 2x * 26x) = 396
(442x + 52x2) = 396

Solving
442x + 52x2 = 396

Solving for variable 'x'.

Reorder the terms:
-396 + 442x + 52x2 = 396 + -396

Combine like terms: 396 + -396 = 0
-396 + 442x + 52x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-198 + 221x + 26x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-198 + 221x + 26x2)' equal to zero and attempt to solve:

Simplifying
-198 + 221x + 26x2 = 0

Solving
-198 + 221x + 26x2 = 0

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

Divide each side by '26'.
-7.615384615 + 8.5x + x2 = 0

Move the constant term to the right:

Add '7.615384615' to each side of the equation.
-7.615384615 + 8.5x + 7.615384615 + x2 = 0 + 7.615384615

Reorder the terms:
-7.615384615 + 7.615384615 + 8.5x + x2 = 0 + 7.615384615

Combine like terms: -7.615384615 + 7.615384615 = 0.000000000
0.000000000 + 8.5x + x2 = 0 + 7.615384615
8.5x + x2 = 0 + 7.615384615

Combine like terms: 0 + 7.615384615 = 7.615384615
8.5x + x2 = 7.615384615

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 7.615384615 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 7.615384615 + 18.0625

Combine like terms: 7.615384615 + 18.0625 = 25.677884615
18.0625 + 8.5x + x2 = 25.677884615

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 25.677884615

Calculate the square root of the right side: 5.06733506

Break this problem into two subproblems by setting 
(x + 4.25) equal to 5.06733506 and -5.06733506.


Subproblem 1
x + 4.25 = 5.06733506

Simplifying
x + 4.25 = 5.06733506

Reorder the terms:
4.25 + x = 5.06733506

Solving
4.25 + x = 5.06733506

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 5.06733506 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 5.06733506 + -4.25
x = 5.06733506 + -4.25

Combine like terms: 5.06733506 + -4.25 = 0.81733506
x = 0.81733506

Simplifying
x = 0.81733506


Subproblem 2
x + 4.25 = -5.06733506

Simplifying
x + 4.25 = -5.06733506

Reorder the terms:
4.25 + x = -5.06733506

Solving
4.25 + x = -5.06733506

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -5.06733506 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -5.06733506 + -4.25
x = -5.06733506 + -4.25

Combine like terms: -5.06733506 + -4.25 = -9.31733506
x = -9.31733506

Simplifying
x = -9.31733506


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.81733506, -9.31733506}
Solution
x = {0.81733506, -9.31733506}

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