(-5x+x)(0.442+x)=0.003

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Solution for (-5x+x)(0.442+x)=0.003 equation: 


Simplifying
(-5x + x)(0.442 + x) = 0.003

Combine like terms: -5x + x = -4x
(-4x)(0.442 + x) = 0.003

Remove parenthesis around (-4x)
-4x(0.442 + x) = 0.003
(0.442 * -4x + x * -4x) = 0.003
(-1.768x + -4x2) = 0.003

Solving
-1.768x + -4x2 = 0.003

Solving for variable 'x'.

Reorder the terms:
-0.003 + -1.768x + -4x2 = 0.003 + -0.003

Combine like terms: 0.003 + -0.003 = 0.000
-0.003 + -1.768x + -4x2 = 0.000

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.00075 + 0.442x + x2 = 0.000

Move the constant term to the right:

Add '-0.00075' to each side of the equation.
0.00075 + 0.442x + -0.00075 + x2 = 0.000 + -0.00075

Reorder the terms:
0.00075 + -0.00075 + 0.442x + x2 = 0.000 + -0.00075

Combine like terms: 0.00075 + -0.00075 = 0.00000
0.00000 + 0.442x + x2 = 0.000 + -0.00075
0.442x + x2 = 0.000 + -0.00075

Combine like terms: 0.000 + -0.00075 = -0.00075
0.442x + x2 = -0.00075

The x term is 0.442x.  Take half its coefficient (0.221).
Square it (0.048841) and add it to both sides.

Add '0.048841' to each side of the equation.
0.442x + 0.048841 + x2 = -0.00075 + 0.048841

Reorder the terms:
0.048841 + 0.442x + x2 = -0.00075 + 0.048841

Combine like terms: -0.00075 + 0.048841 = 0.048091
0.048841 + 0.442x + x2 = 0.048091

Factor a perfect square on the left side:
(x + 0.221)(x + 0.221) = 0.048091

Calculate the square root of the right side: 0.219296603

Break this problem into two subproblems by setting 
(x + 0.221) equal to 0.219296603 and -0.219296603.


Subproblem 1
x + 0.221 = 0.219296603

Simplifying
x + 0.221 = 0.219296603

Reorder the terms:
0.221 + x = 0.219296603

Solving
0.221 + x = 0.219296603

Solving for variable 'x'.

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

Add '-0.221' to each side of the equation.
0.221 + -0.221 + x = 0.219296603 + -0.221

Combine like terms: 0.221 + -0.221 = 0.000
0.000 + x = 0.219296603 + -0.221
x = 0.219296603 + -0.221

Combine like terms: 0.219296603 + -0.221 = -0.001703397
x = -0.001703397

Simplifying
x = -0.001703397


Subproblem 2
x + 0.221 = -0.219296603

Simplifying
x + 0.221 = -0.219296603

Reorder the terms:
0.221 + x = -0.219296603

Solving
0.221 + x = -0.219296603

Solving for variable 'x'.

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

Add '-0.221' to each side of the equation.
0.221 + -0.221 + x = -0.219296603 + -0.221

Combine like terms: 0.221 + -0.221 = 0.000
0.000 + x = -0.219296603 + -0.221
x = -0.219296603 + -0.221

Combine like terms: -0.219296603 + -0.221 = -0.440296603
x = -0.440296603

Simplifying
x = -0.440296603


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.001703397, -0.440296603}

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