(5x+x)(0.422-x)=0.003

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Solution for (5x+x)(0.422-x)=0.003 equation: 


Simplifying
(5x + x)(0.422 + -1x) = 0.003

Combine like terms: 5x + x = 6x
(6x)(0.422 + -1x) = 0.003

Remove parenthesis around (6x)
6x(0.422 + -1x) = 0.003
(0.422 * 6x + -1x * 6x) = 0.003
(2.532x + -6x2) = 0.003

Solving
2.532x + -6x2 = 0.003

Solving for variable 'x'.

Reorder the terms:
-0.003 + 2.532x + -6x2 = 0.003 + -0.003

Combine like terms: 0.003 + -0.003 = 0.000
-0.003 + 2.532x + -6x2 = 0.000

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.0005 + -0.422x + x2 = 0.000

Move the constant term to the right:

Add '-0.0005' to each side of the equation.
0.0005 + -0.422x + -0.0005 + x2 = 0.000 + -0.0005

Reorder the terms:
0.0005 + -0.0005 + -0.422x + x2 = 0.000 + -0.0005

Combine like terms: 0.0005 + -0.0005 = 0.0000
0.0000 + -0.422x + x2 = 0.000 + -0.0005
-0.422x + x2 = 0.000 + -0.0005

Combine like terms: 0.000 + -0.0005 = -0.0005
-0.422x + x2 = -0.0005

The x term is -0.422x.  Take half its coefficient (-0.211).
Square it (0.044521) and add it to both sides.

Add '0.044521' to each side of the equation.
-0.422x + 0.044521 + x2 = -0.0005 + 0.044521

Reorder the terms:
0.044521 + -0.422x + x2 = -0.0005 + 0.044521

Combine like terms: -0.0005 + 0.044521 = 0.044021
0.044521 + -0.422x + x2 = 0.044021

Factor a perfect square on the left side:
(x + -0.211)(x + -0.211) = 0.044021

Calculate the square root of the right side: 0.20981182

Break this problem into two subproblems by setting 
(x + -0.211) equal to 0.20981182 and -0.20981182.


Subproblem 1
x + -0.211 = 0.20981182

Simplifying
x + -0.211 = 0.20981182

Reorder the terms:
-0.211 + x = 0.20981182

Solving
-0.211 + x = 0.20981182

Solving for variable 'x'.

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

Add '0.211' to each side of the equation.
-0.211 + 0.211 + x = 0.20981182 + 0.211

Combine like terms: -0.211 + 0.211 = 0.000
0.000 + x = 0.20981182 + 0.211
x = 0.20981182 + 0.211

Combine like terms: 0.20981182 + 0.211 = 0.42081182
x = 0.42081182

Simplifying
x = 0.42081182


Subproblem 2
x + -0.211 = -0.20981182

Simplifying
x + -0.211 = -0.20981182

Reorder the terms:
-0.211 + x = -0.20981182

Solving
-0.211 + x = -0.20981182

Solving for variable 'x'.

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

Add '0.211' to each side of the equation.
-0.211 + 0.211 + x = -0.20981182 + 0.211

Combine like terms: -0.211 + 0.211 = 0.000
0.000 + x = -0.20981182 + 0.211
x = -0.20981182 + 0.211

Combine like terms: -0.20981182 + 0.211 = 0.00118818
x = 0.00118818

Simplifying
x = 0.00118818


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.42081182, 0.00118818}

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