(0.937)(0.4-x)(2.2-x)=(x)(1.6+x)

Solution for (0.937)(0.4-x)(2.2-x)=(x)(1.6+x) equation:

Simplifying
(0.937)(0.4 + -1x)(2.2 + -1x) = (x)(1.6 + x)

Multiply (0.4 + -1x) * (2.2 + -1x)
0.937(0.4(2.2 + -1x) + -1x * (2.2 + -1x)) = (x)(1.6 + x)
0.937((2.2 * 0.4 + -1x * 0.4) + -1x * (2.2 + -1x)) = (x)(1.6 + x)
0.937((0.88 + -0.4x) + -1x * (2.2 + -1x)) = (x)(1.6 + x)
0.937(0.88 + -0.4x + (2.2 * -1x + -1x * -1x)) = (x)(1.6 + x)
0.937(0.88 + -0.4x + (-2.2x + 1x2)) = (x)(1.6 + x)

Combine like terms: -0.4x + -2.2x = -2.6x
0.937(0.88 + -2.6x + 1x2) = (x)(1.6 + x)
(0.88 * 0.937 + -2.6x * 0.937 + 1x2 * 0.937) = (x)(1.6 + x)
(0.82456 + -2.4362x + 0.937x2) = (x)(1.6 + x)
0.82456 + -2.4362x + 0.937x2 = (1.6 * x + x * x)
0.82456 + -2.4362x + 0.937x2 = (1.6x + x2)

Solving
0.82456 + -2.4362x + 0.937x2 = 1.6x + x2

Solving for variable 'x'.

Reorder the terms:
0.82456 + -2.4362x + -1.6x + 0.937x2 + -1x2 = 1.6x + x2 + -1.6x + -1x2

Combine like terms: -2.4362x + -1.6x = -4.0362x
0.82456 + -4.0362x + 0.937x2 + -1x2 = 1.6x + x2 + -1.6x + -1x2

Combine like terms: 0.937x2 + -1x2 = -0.063x2
0.82456 + -4.0362x + -0.063x2 = 1.6x + x2 + -1.6x + -1x2

Reorder the terms:
0.82456 + -4.0362x + -0.063x2 = 1.6x + -1.6x + x2 + -1x2

Combine like terms: 1.6x + -1.6x = 0.0
0.82456 + -4.0362x + -0.063x2 = 0.0 + x2 + -1x2
0.82456 + -4.0362x + -0.063x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.82456 + -4.0362x + -0.063x2 = 0

Begin completing the square.  Divide all terms by
-0.063 the coefficient of the squared term: 

Divide each side by '-0.063'.
-13.08825397 + 64.06666667x + x2 = 0

Move the constant term to the right:

Add '13.08825397' to each side of the equation.
-13.08825397 + 64.06666667x + 13.08825397 + x2 = 0 + 13.08825397

Reorder the terms:
-13.08825397 + 13.08825397 + 64.06666667x + x2 = 0 + 13.08825397

Combine like terms: -13.08825397 + 13.08825397 = 0.00000000
0.00000000 + 64.06666667x + x2 = 0 + 13.08825397
64.06666667x + x2 = 0 + 13.08825397

Combine like terms: 0 + 13.08825397 = 13.08825397
64.06666667x + x2 = 13.08825397

The x term is 64.06666667x.  Take half its coefficient (32.03333334).
Square it (1026.134445) and add it to both sides.

Add '1026.134445' to each side of the equation.
64.06666667x + 1026.134445 + x2 = 13.08825397 + 1026.134445

Reorder the terms:
1026.134445 + 64.06666667x + x2 = 13.08825397 + 1026.134445

Combine like terms: 13.08825397 + 1026.134445 = 1039.22269897
1026.134445 + 64.06666667x + x2 = 1039.22269897

Factor a perfect square on the left side:
(x + 32.03333334)(x + 32.03333334) = 1039.22269897

Calculate the square root of the right side: 32.2369772

Break this problem into two subproblems by setting 
(x + 32.03333334) equal to 32.2369772 and -32.2369772.

Subproblem 1
x + 32.03333334 = 32.2369772

Simplifying
x + 32.03333334 = 32.2369772

Reorder the terms:
32.03333334 + x = 32.2369772

Solving
32.03333334 + x = 32.2369772

Solving for variable 'x'.

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

Add '-32.03333334' to each side of the equation.
32.03333334 + -32.03333334 + x = 32.2369772 + -32.03333334

Combine like terms: 32.03333334 + -32.03333334 = 0.00000000
0.00000000 + x = 32.2369772 + -32.03333334
x = 32.2369772 + -32.03333334

Combine like terms: 32.2369772 + -32.03333334 = 0.20364386
x = 0.20364386

Simplifying
x = 0.20364386

Subproblem 2
x + 32.03333334 = -32.2369772

Simplifying
x + 32.03333334 = -32.2369772

Reorder the terms:
32.03333334 + x = -32.2369772

Solving
32.03333334 + x = -32.2369772

Solving for variable 'x'.

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

Add '-32.03333334' to each side of the equation.
32.03333334 + -32.03333334 + x = -32.2369772 + -32.03333334

Combine like terms: 32.03333334 + -32.03333334 = 0.00000000
0.00000000 + x = -32.2369772 + -32.03333334
x = -32.2369772 + -32.03333334

Combine like terms: -32.2369772 + -32.03333334 = -64.27031054
x = -64.27031054

Simplifying
x = -64.27031054

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.20364386, -64.27031054}