40x+25x(68-x)=33

Solution for 40x+25x(68-x)=33 equation:

Simplifying
40x + 25x(68 + -1x) = 33
40x + (68 * 25x + -1x * 25x) = 33
40x + (1700x + -25x2) = 33

Combine like terms: 40x + 1700x = 1740x
1740x + -25x2 = 33

Solving
1740x + -25x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + 1740x + -25x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 1740x + -25x2 = 0

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
1.32 + -69.6x + x2 = 0

Move the constant term to the right:

Add '-1.32' to each side of the equation.
1.32 + -69.6x + -1.32 + x2 = 0 + -1.32

Reorder the terms:
1.32 + -1.32 + -69.6x + x2 = 0 + -1.32

Combine like terms: 1.32 + -1.32 = 0.00
0.00 + -69.6x + x2 = 0 + -1.32
-69.6x + x2 = 0 + -1.32

Combine like terms: 0 + -1.32 = -1.32
-69.6x + x2 = -1.32

The x term is -69.6x.  Take half its coefficient (-34.8).
Square it (1211.04) and add it to both sides.

Add '1211.04' to each side of the equation.
-69.6x + 1211.04 + x2 = -1.32 + 1211.04

Reorder the terms:
1211.04 + -69.6x + x2 = -1.32 + 1211.04

Combine like terms: -1.32 + 1211.04 = 1209.72
1211.04 + -69.6x + x2 = 1209.72

Factor a perfect square on the left side:
(x + -34.8)(x + -34.8) = 1209.72

Calculate the square root of the right side: 34.781029312

Break this problem into two subproblems by setting 
(x + -34.8) equal to 34.781029312 and -34.781029312.

Subproblem 1
x + -34.8 = 34.781029312

Simplifying
x + -34.8 = 34.781029312

Reorder the terms:
-34.8 + x = 34.781029312

Solving
-34.8 + x = 34.781029312

Solving for variable 'x'.

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

Add '34.8' to each side of the equation.
-34.8 + 34.8 + x = 34.781029312 + 34.8

Combine like terms: -34.8 + 34.8 = 0.0
0.0 + x = 34.781029312 + 34.8
x = 34.781029312 + 34.8

Combine like terms: 34.781029312 + 34.8 = 69.581029312
x = 69.581029312

Simplifying
x = 69.581029312

Subproblem 2
x + -34.8 = -34.781029312

Simplifying
x + -34.8 = -34.781029312

Reorder the terms:
-34.8 + x = -34.781029312

Solving
-34.8 + x = -34.781029312

Solving for variable 'x'.

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

Add '34.8' to each side of the equation.
-34.8 + 34.8 + x = -34.781029312 + 34.8

Combine like terms: -34.8 + 34.8 = 0.0
0.0 + x = -34.781029312 + 34.8
x = -34.781029312 + 34.8

Combine like terms: -34.781029312 + 34.8 = 0.018970688
x = 0.018970688

Simplifying
x = 0.018970688

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {69.581029312, 0.018970688}