2x+4x(38-x)=136

Solution for 2x+4x(38-x)=136 equation:

Simplifying
2x + 4x(38 + -1x) = 136
2x + (38 * 4x + -1x * 4x) = 136
2x + (152x + -4x2) = 136

Combine like terms: 2x + 152x = 154x
154x + -4x2 = 136

Solving
154x + -4x2 = 136

Solving for variable 'x'.

Reorder the terms:
-136 + 154x + -4x2 = 136 + -136

Combine like terms: 136 + -136 = 0
-136 + 154x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + 77x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-68 + 77x + -2x2)' equal to zero and attempt to solve:

Simplifying
-68 + 77x + -2x2 = 0

Solving
-68 + 77x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
34 + -38.5x + x2 = 0

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -38.5x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -38.5x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -38.5x + x2 = 0 + -34
-38.5x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-38.5x + x2 = -34

The x term is -38.5x.  Take half its coefficient (-19.25).
Square it (370.5625) and add it to both sides.

Add '370.5625' to each side of the equation.
-38.5x + 370.5625 + x2 = -34 + 370.5625

Reorder the terms:
370.5625 + -38.5x + x2 = -34 + 370.5625

Combine like terms: -34 + 370.5625 = 336.5625
370.5625 + -38.5x + x2 = 336.5625

Factor a perfect square on the left side:
(x + -19.25)(x + -19.25) = 336.5625

Calculate the square root of the right side: 18.345639809

Break this problem into two subproblems by setting 
(x + -19.25) equal to 18.345639809 and -18.345639809.

Subproblem 1
x + -19.25 = 18.345639809

Simplifying
x + -19.25 = 18.345639809

Reorder the terms:
-19.25 + x = 18.345639809

Solving
-19.25 + x = 18.345639809

Solving for variable 'x'.

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

Add '19.25' to each side of the equation.
-19.25 + 19.25 + x = 18.345639809 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + x = 18.345639809 + 19.25
x = 18.345639809 + 19.25

Combine like terms: 18.345639809 + 19.25 = 37.595639809
x = 37.595639809

Simplifying
x = 37.595639809

Subproblem 2
x + -19.25 = -18.345639809

Simplifying
x + -19.25 = -18.345639809

Reorder the terms:
-19.25 + x = -18.345639809

Solving
-19.25 + x = -18.345639809

Solving for variable 'x'.

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

Add '19.25' to each side of the equation.
-19.25 + 19.25 + x = -18.345639809 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + x = -18.345639809 + 19.25
x = -18.345639809 + 19.25

Combine like terms: -18.345639809 + 19.25 = 0.904360191
x = 0.904360191

Simplifying
x = 0.904360191

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.595639809, 0.904360191}
Solution
x = {37.595639809, 0.904360191}