38=2(2x+4)2x

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Solution for 38=2(2x+4)2x equation: 


Simplifying
38 = 2(2x + 4) * 2x

Reorder the terms:
38 = 2(4 + 2x) * 2x

Reorder the terms for easier multiplication:
38 = 2 * 2x(4 + 2x)

Multiply 2 * 2
38 = 4x(4 + 2x)
38 = (4 * 4x + 2x * 4x)
38 = (16x + 8x2)

Solving
38 = 16x + 8x2

Solving for variable 'x'.

Reorder the terms:
38 + -16x + -8x2 = 16x + -16x + 8x2 + -8x2

Combine like terms: 16x + -16x = 0
38 + -16x + -8x2 = 0 + 8x2 + -8x2
38 + -16x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
38 + -16x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(19 + -8x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(19 + -8x + -4x2)' equal to zero and attempt to solve:

Simplifying
19 + -8x + -4x2 = 0

Solving
19 + -8x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-4.75 + 2x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 2x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 2x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 2x + x2 = 0 + 4.75
2x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
2x + x2 = 4.75

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 4.75 + 1

Reorder the terms:
1 + 2x + x2 = 4.75 + 1

Combine like terms: 4.75 + 1 = 5.75
1 + 2x + x2 = 5.75

Factor a perfect square on the left side:
(x + 1)(x + 1) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + 1) equal to 2.397915762 and -2.397915762.


Subproblem 1
x + 1 = 2.397915762

Simplifying
x + 1 = 2.397915762

Reorder the terms:
1 + x = 2.397915762

Solving
1 + x = 2.397915762

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.397915762 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.397915762 + -1
x = 2.397915762 + -1

Combine like terms: 2.397915762 + -1 = 1.397915762
x = 1.397915762

Simplifying
x = 1.397915762


Subproblem 2
x + 1 = -2.397915762

Simplifying
x + 1 = -2.397915762

Reorder the terms:
1 + x = -2.397915762

Solving
1 + x = -2.397915762

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.397915762 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.397915762 + -1
x = -2.397915762 + -1

Combine like terms: -2.397915762 + -1 = -3.397915762
x = -3.397915762

Simplifying
x = -3.397915762


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.397915762, -3.397915762}
Solution
x = {1.397915762, -3.397915762}

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