4.1x(x-0.2)+3.3x=0.4(x-1)+2.1

Solution for 4.1x(x-0.2)+3.3x=0.4(x-1)+2.1 equation:

Simplifying
4.1x(x + -0.2) + 3.3x = 0.4(x + -1) + 2.1

Reorder the terms:
4.1x(-0.2 + x) + 3.3x = 0.4(x + -1) + 2.1
(-0.2 * 4.1x + x * 4.1x) + 3.3x = 0.4(x + -1) + 2.1
(-0.82x + 4.1x2) + 3.3x = 0.4(x + -1) + 2.1

Reorder the terms:
-0.82x + 3.3x + 4.1x2 = 0.4(x + -1) + 2.1

Combine like terms: -0.82x + 3.3x = 2.48x
2.48x + 4.1x2 = 0.4(x + -1) + 2.1

Reorder the terms:
2.48x + 4.1x2 = 0.4(-1 + x) + 2.1
2.48x + 4.1x2 = (-1 * 0.4 + x * 0.4) + 2.1
2.48x + 4.1x2 = (-0.4 + 0.4x) + 2.1

Reorder the terms:
2.48x + 4.1x2 = -0.4 + 2.1 + 0.4x

Combine like terms: -0.4 + 2.1 = 1.7
2.48x + 4.1x2 = 1.7 + 0.4x

Solving
2.48x + 4.1x2 = 1.7 + 0.4x

Solving for variable 'x'.

Reorder the terms:
-1.7 + 2.48x + -0.4x + 4.1x2 = 1.7 + 0.4x + -1.7 + -0.4x

Combine like terms: 2.48x + -0.4x = 2.08x
-1.7 + 2.08x + 4.1x2 = 1.7 + 0.4x + -1.7 + -0.4x

Reorder the terms:
-1.7 + 2.08x + 4.1x2 = 1.7 + -1.7 + 0.4x + -0.4x

Combine like terms: 1.7 + -1.7 = 0.0
-1.7 + 2.08x + 4.1x2 = 0.0 + 0.4x + -0.4x
-1.7 + 2.08x + 4.1x2 = 0.4x + -0.4x

Combine like terms: 0.4x + -0.4x = 0.0
-1.7 + 2.08x + 4.1x2 = 0.0

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

Divide each side by '4.1'.
-0.4146341463 + 0.5073170732x + x2 = 0

Move the constant term to the right:

Add '0.4146341463' to each side of the equation.
-0.4146341463 + 0.5073170732x + 0.4146341463 + x2 = 0 + 0.4146341463

Reorder the terms:
-0.4146341463 + 0.4146341463 + 0.5073170732x + x2 = 0 + 0.4146341463

Combine like terms: -0.4146341463 + 0.4146341463 = 0.0000000000
0.0000000000 + 0.5073170732x + x2 = 0 + 0.4146341463
0.5073170732x + x2 = 0 + 0.4146341463

Combine like terms: 0 + 0.4146341463 = 0.4146341463
0.5073170732x + x2 = 0.4146341463

The x term is 0.5073170732x.  Take half its coefficient (0.2536585366).
Square it (0.06434265319) and add it to both sides.

Add '0.06434265319' to each side of the equation.
0.5073170732x + 0.06434265319 + x2 = 0.4146341463 + 0.06434265319

Reorder the terms:
0.06434265319 + 0.5073170732x + x2 = 0.4146341463 + 0.06434265319

Combine like terms: 0.4146341463 + 0.06434265319 = 0.47897679949
0.06434265319 + 0.5073170732x + x2 = 0.47897679949

Factor a perfect square on the left side:
(x + 0.2536585366)(x + 0.2536585366) = 0.47897679949

Calculate the square root of the right side: 0.692081498

Break this problem into two subproblems by setting 
(x + 0.2536585366) equal to 0.692081498 and -0.692081498.

Subproblem 1
x + 0.2536585366 = 0.692081498

Simplifying
x + 0.2536585366 = 0.692081498

Reorder the terms:
0.2536585366 + x = 0.692081498

Solving
0.2536585366 + x = 0.692081498

Solving for variable 'x'.

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

Add '-0.2536585366' to each side of the equation.
0.2536585366 + -0.2536585366 + x = 0.692081498 + -0.2536585366

Combine like terms: 0.2536585366 + -0.2536585366 = 0.0000000000
0.0000000000 + x = 0.692081498 + -0.2536585366
x = 0.692081498 + -0.2536585366

Combine like terms: 0.692081498 + -0.2536585366 = 0.4384229614
x = 0.4384229614

Simplifying
x = 0.4384229614

Subproblem 2
x + 0.2536585366 = -0.692081498

Simplifying
x + 0.2536585366 = -0.692081498

Reorder the terms:
0.2536585366 + x = -0.692081498

Solving
0.2536585366 + x = -0.692081498

Solving for variable 'x'.

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

Add '-0.2536585366' to each side of the equation.
0.2536585366 + -0.2536585366 + x = -0.692081498 + -0.2536585366

Combine like terms: 0.2536585366 + -0.2536585366 = 0.0000000000
0.0000000000 + x = -0.692081498 + -0.2536585366
x = -0.692081498 + -0.2536585366

Combine like terms: -0.692081498 + -0.2536585366 = -0.9457400346
x = -0.9457400346

Simplifying
x = -0.9457400346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4384229614, -0.9457400346}