0.054575751x^2-0.301606772x+0.001031021=0

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Solution for 0.054575751x^2-0.301606772x+0.001031021=0 equation: 


Simplifying
0.054575751x2 + -0.301606772x + 0.001031021 = 0

Reorder the terms:
0.001031021 + -0.301606772x + 0.054575751x2 = 0

Solving
0.001031021 + -0.301606772x + 0.054575751x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.054575751 the coefficient of the squared term: 

Divide each side by '0.054575751'.
0.01889155863 + -5.526387937x + x2 = 0

Move the constant term to the right:

Add '-0.01889155863' to each side of the equation.
0.01889155863 + -5.526387937x + -0.01889155863 + x2 = 0 + -0.01889155863

Reorder the terms:
0.01889155863 + -0.01889155863 + -5.526387937x + x2 = 0 + -0.01889155863

Combine like terms: 0.01889155863 + -0.01889155863 = 0.00000000000
0.00000000000 + -5.526387937x + x2 = 0 + -0.01889155863
-5.526387937x + x2 = 0 + -0.01889155863

Combine like terms: 0 + -0.01889155863 = -0.01889155863
-5.526387937x + x2 = -0.01889155863

The x term is -5.526387937x.  Take half its coefficient (-2.763193969).
Square it (7.635240910) and add it to both sides.

Add '7.635240910' to each side of the equation.
-5.526387937x + 7.635240910 + x2 = -0.01889155863 + 7.635240910

Reorder the terms:
7.635240910 + -5.526387937x + x2 = -0.01889155863 + 7.635240910

Combine like terms: -0.01889155863 + 7.635240910 = 7.61634935137
7.635240910 + -5.526387937x + x2 = 7.61634935137

Factor a perfect square on the left side:
(x + -2.763193969)(x + -2.763193969) = 7.61634935137

Calculate the square root of the right side: 2.759773424

Break this problem into two subproblems by setting 
(x + -2.763193969) equal to 2.759773424 and -2.759773424.


Subproblem 1
x + -2.763193969 = 2.759773424

Simplifying
x + -2.763193969 = 2.759773424

Reorder the terms:
-2.763193969 + x = 2.759773424

Solving
-2.763193969 + x = 2.759773424

Solving for variable 'x'.

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

Add '2.763193969' to each side of the equation.
-2.763193969 + 2.763193969 + x = 2.759773424 + 2.763193969

Combine like terms: -2.763193969 + 2.763193969 = 0.000000000
0.000000000 + x = 2.759773424 + 2.763193969
x = 2.759773424 + 2.763193969

Combine like terms: 2.759773424 + 2.763193969 = 5.522967393
x = 5.522967393

Simplifying
x = 5.522967393


Subproblem 2
x + -2.763193969 = -2.759773424

Simplifying
x + -2.763193969 = -2.759773424

Reorder the terms:
-2.763193969 + x = -2.759773424

Solving
-2.763193969 + x = -2.759773424

Solving for variable 'x'.

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

Add '2.763193969' to each side of the equation.
-2.763193969 + 2.763193969 + x = -2.759773424 + 2.763193969

Combine like terms: -2.763193969 + 2.763193969 = 0.000000000
0.000000000 + x = -2.759773424 + 2.763193969
x = -2.759773424 + 2.763193969

Combine like terms: -2.759773424 + 2.763193969 = 0.003420545
x = 0.003420545

Simplifying
x = 0.003420545


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.522967393, 0.003420545}

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