0.04x^2-0.5x+0.05=0

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Solution for 0.04x^2-0.5x+0.05=0 equation: 


Simplifying
0.04x2 + -0.5x + 0.05 = 0

Reorder the terms:
0.05 + -0.5x + 0.04x2 = 0

Solving
0.05 + -0.5x + 0.04x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.04'.
1.25 + -12.5x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -12.5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -12.5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -12.5x + x2 = 0 + -1.25
-12.5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-12.5x + x2 = -1.25

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -1.25 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -1.25 + 39.0625

Combine like terms: -1.25 + 39.0625 = 37.8125
39.0625 + -12.5x + x2 = 37.8125

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 37.8125

Calculate the square root of the right side: 6.149186938

Break this problem into two subproblems by setting 
(x + -6.25) equal to 6.149186938 and -6.149186938.


Subproblem 1
x + -6.25 = 6.149186938

Simplifying
x + -6.25 = 6.149186938

Reorder the terms:
-6.25 + x = 6.149186938

Solving
-6.25 + x = 6.149186938

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 6.149186938 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 6.149186938 + 6.25
x = 6.149186938 + 6.25

Combine like terms: 6.149186938 + 6.25 = 12.399186938
x = 12.399186938

Simplifying
x = 12.399186938


Subproblem 2
x + -6.25 = -6.149186938

Simplifying
x + -6.25 = -6.149186938

Reorder the terms:
-6.25 + x = -6.149186938

Solving
-6.25 + x = -6.149186938

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -6.149186938 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -6.149186938 + 6.25
x = -6.149186938 + 6.25

Combine like terms: -6.149186938 + 6.25 = 0.100813062
x = 0.100813062

Simplifying
x = 0.100813062


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.399186938, 0.100813062}

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