(0.791)(x)(3.4-x)=(2.6-x)(4.0-x)

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Solution for (0.791)(x)(3.4-x)=(2.6-x)(4.0-x) equation: 


Simplifying
(0.791)(x)(3.4 + -1x) = (2.6 + -1x)(4.0 + -1x)
(3.4 * 0.791x + -1x * 0.791x) = (2.6 + -1x)(4.0 + -1x)
(2.6894x + -0.791x2) = (2.6 + -1x)(4.0 + -1x)

Multiply (2.6 + -1x) * (4.0 + -1x)
2.6894x + -0.791x2 = (2.6(4.0 + -1x) + -1x * (4.0 + -1x))
2.6894x + -0.791x2 = ((4.0 * 2.6 + -1x * 2.6) + -1x * (4.0 + -1x))
2.6894x + -0.791x2 = ((10.4 + -2.6x) + -1x * (4.0 + -1x))
2.6894x + -0.791x2 = (10.4 + -2.6x + (4.0 * -1x + -1x * -1x))
2.6894x + -0.791x2 = (10.4 + -2.6x + (-4x + 1x2))

Combine like terms: -2.6x + -4x = -6.6x
2.6894x + -0.791x2 = (10.4 + -6.6x + 1x2)

Solving
2.6894x + -0.791x2 = 10.4 + -6.6x + 1x2

Solving for variable 'x'.

Reorder the terms:
-10.4 + 2.6894x + 6.6x + -0.791x2 + -1x2 = 10.4 + -6.6x + 1x2 + -10.4 + 6.6x + -1x2

Combine like terms: 2.6894x + 6.6x = 9.2894x
-10.4 + 9.2894x + -0.791x2 + -1x2 = 10.4 + -6.6x + 1x2 + -10.4 + 6.6x + -1x2

Combine like terms: -0.791x2 + -1x2 = -1.791x2
-10.4 + 9.2894x + -1.791x2 = 10.4 + -6.6x + 1x2 + -10.4 + 6.6x + -1x2

Reorder the terms:
-10.4 + 9.2894x + -1.791x2 = 10.4 + -10.4 + -6.6x + 6.6x + 1x2 + -1x2

Combine like terms: 10.4 + -10.4 = 0.0
-10.4 + 9.2894x + -1.791x2 = 0.0 + -6.6x + 6.6x + 1x2 + -1x2
-10.4 + 9.2894x + -1.791x2 = -6.6x + 6.6x + 1x2 + -1x2

Combine like terms: -6.6x + 6.6x = 0.0
-10.4 + 9.2894x + -1.791x2 = 0.0 + 1x2 + -1x2
-10.4 + 9.2894x + -1.791x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-10.4 + 9.2894x + -1.791x2 = 0

Begin completing the square.  Divide all terms by
-1.791 the coefficient of the squared term: 

Divide each side by '-1.791'.
5.806811837 + -5.186711334x + x2 = 0

Move the constant term to the right:

Add '-5.806811837' to each side of the equation.
5.806811837 + -5.186711334x + -5.806811837 + x2 = 0 + -5.806811837

Reorder the terms:
5.806811837 + -5.806811837 + -5.186711334x + x2 = 0 + -5.806811837

Combine like terms: 5.806811837 + -5.806811837 = 0.000000000
0.000000000 + -5.186711334x + x2 = 0 + -5.806811837
-5.186711334x + x2 = 0 + -5.806811837

Combine like terms: 0 + -5.806811837 = -5.806811837
-5.186711334x + x2 = -5.806811837

The x term is -5.186711334x.  Take half its coefficient (-2.593355667).
Square it (6.725493616) and add it to both sides.

Add '6.725493616' to each side of the equation.
-5.186711334x + 6.725493616 + x2 = -5.806811837 + 6.725493616

Reorder the terms:
6.725493616 + -5.186711334x + x2 = -5.806811837 + 6.725493616

Combine like terms: -5.806811837 + 6.725493616 = 0.918681779
6.725493616 + -5.186711334x + x2 = 0.918681779

Factor a perfect square on the left side:
(x + -2.593355667)(x + -2.593355667) = 0.918681779

Calculate the square root of the right side: 0.958478888

Break this problem into two subproblems by setting 
(x + -2.593355667) equal to 0.958478888 and -0.958478888.


Subproblem 1
x + -2.593355667 = 0.958478888

Simplifying
x + -2.593355667 = 0.958478888

Reorder the terms:
-2.593355667 + x = 0.958478888

Solving
-2.593355667 + x = 0.958478888

Solving for variable 'x'.

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

Add '2.593355667' to each side of the equation.
-2.593355667 + 2.593355667 + x = 0.958478888 + 2.593355667

Combine like terms: -2.593355667 + 2.593355667 = 0.000000000
0.000000000 + x = 0.958478888 + 2.593355667
x = 0.958478888 + 2.593355667

Combine like terms: 0.958478888 + 2.593355667 = 3.551834555
x = 3.551834555

Simplifying
x = 3.551834555


Subproblem 2
x + -2.593355667 = -0.958478888

Simplifying
x + -2.593355667 = -0.958478888

Reorder the terms:
-2.593355667 + x = -0.958478888

Solving
-2.593355667 + x = -0.958478888

Solving for variable 'x'.

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

Add '2.593355667' to each side of the equation.
-2.593355667 + 2.593355667 + x = -0.958478888 + 2.593355667

Combine like terms: -2.593355667 + 2.593355667 = 0.000000000
0.000000000 + x = -0.958478888 + 2.593355667
x = -0.958478888 + 2.593355667

Combine like terms: -0.958478888 + 2.593355667 = 1.634876779
x = 1.634876779

Simplifying
x = 1.634876779


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.551834555, 1.634876779}

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