x^2-x*0.0188-0.05=0

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Solution for x^2-x*0.0188-0.05=0 equation: 


Simplifying
x2 + -1x * 0.0188 + -0.05 = 0

Reorder the terms for easier multiplication:
x2 + -1 * 0.0188x + -0.05 = 0

Multiply -1 * 0.0188
x2 + -0.0188x + -0.05 = 0

Reorder the terms:
-0.05 + -0.0188x + x2 = 0

Solving
-0.05 + -0.0188x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -0.0188x + 0.05 + x2 = 0 + 0.05

Reorder the terms:
-0.05 + 0.05 + -0.0188x + x2 = 0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -0.0188x + x2 = 0 + 0.05
-0.0188x + x2 = 0 + 0.05

Combine like terms: 0 + 0.05 = 0.05
-0.0188x + x2 = 0.05

The x term is -0.0188x.  Take half its coefficient (-0.0094).
Square it (0.00008836) and add it to both sides.

Add '0.00008836' to each side of the equation.
-0.0188x + 0.00008836 + x2 = 0.05 + 0.00008836

Reorder the terms:
0.00008836 + -0.0188x + x2 = 0.05 + 0.00008836

Combine like terms: 0.05 + 0.00008836 = 0.05008836
0.00008836 + -0.0188x + x2 = 0.05008836

Factor a perfect square on the left side:
(x + -0.0094)(x + -0.0094) = 0.05008836

Calculate the square root of the right side: 0.22380429

Break this problem into two subproblems by setting 
(x + -0.0094) equal to 0.22380429 and -0.22380429.


Subproblem 1
x + -0.0094 = 0.22380429

Simplifying
x + -0.0094 = 0.22380429

Reorder the terms:
-0.0094 + x = 0.22380429

Solving
-0.0094 + x = 0.22380429

Solving for variable 'x'.

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

Add '0.0094' to each side of the equation.
-0.0094 + 0.0094 + x = 0.22380429 + 0.0094

Combine like terms: -0.0094 + 0.0094 = 0.0000
0.0000 + x = 0.22380429 + 0.0094
x = 0.22380429 + 0.0094

Combine like terms: 0.22380429 + 0.0094 = 0.23320429
x = 0.23320429

Simplifying
x = 0.23320429


Subproblem 2
x + -0.0094 = -0.22380429

Simplifying
x + -0.0094 = -0.22380429

Reorder the terms:
-0.0094 + x = -0.22380429

Solving
-0.0094 + x = -0.22380429

Solving for variable 'x'.

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

Add '0.0094' to each side of the equation.
-0.0094 + 0.0094 + x = -0.22380429 + 0.0094

Combine like terms: -0.0094 + 0.0094 = 0.0000
0.0000 + x = -0.22380429 + 0.0094
x = -0.22380429 + 0.0094

Combine like terms: -0.22380429 + 0.0094 = -0.21440429
x = -0.21440429

Simplifying
x = -0.21440429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.23320429, -0.21440429}

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