X^2+0.001X-0.053=0

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Solution for X^2+0.001X-0.053=0 equation: 


Simplifying
X2 + 0.001X + -0.053 = 0

Reorder the terms:
-0.053 + 0.001X + X2 = 0

Solving
-0.053 + 0.001X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.053' to each side of the equation.
-0.053 + 0.001X + 0.053 + X2 = 0 + 0.053

Reorder the terms:
-0.053 + 0.053 + 0.001X + X2 = 0 + 0.053

Combine like terms: -0.053 + 0.053 = 0.000
0.000 + 0.001X + X2 = 0 + 0.053
0.001X + X2 = 0 + 0.053

Combine like terms: 0 + 0.053 = 0.053
0.001X + X2 = 0.053

The X term is 0.001X.  Take half its coefficient (0.0005).
Square it (0.00000025) and add it to both sides.

Add '0.00000025' to each side of the equation.
0.001X + 0.00000025 + X2 = 0.053 + 0.00000025

Reorder the terms:
0.00000025 + 0.001X + X2 = 0.053 + 0.00000025

Combine like terms: 0.053 + 0.00000025 = 0.05300025
0.00000025 + 0.001X + X2 = 0.05300025

Factor a perfect square on the left side:
(X + 0.0005)(X + 0.0005) = 0.05300025

Calculate the square root of the right side: 0.230217832

Break this problem into two subproblems by setting 
(X + 0.0005) equal to 0.230217832 and -0.230217832.


Subproblem 1
X + 0.0005 = 0.230217832

Simplifying
X + 0.0005 = 0.230217832

Reorder the terms:
0.0005 + X = 0.230217832

Solving
0.0005 + X = 0.230217832

Solving for variable 'X'.

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

Add '-0.0005' to each side of the equation.
0.0005 + -0.0005 + X = 0.230217832 + -0.0005

Combine like terms: 0.0005 + -0.0005 = 0.0000
0.0000 + X = 0.230217832 + -0.0005
X = 0.230217832 + -0.0005

Combine like terms: 0.230217832 + -0.0005 = 0.229717832
X = 0.229717832

Simplifying
X = 0.229717832


Subproblem 2
X + 0.0005 = -0.230217832

Simplifying
X + 0.0005 = -0.230217832

Reorder the terms:
0.0005 + X = -0.230217832

Solving
0.0005 + X = -0.230217832

Solving for variable 'X'.

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

Add '-0.0005' to each side of the equation.
0.0005 + -0.0005 + X = -0.230217832 + -0.0005

Combine like terms: 0.0005 + -0.0005 = 0.0000
0.0000 + X = -0.230217832 + -0.0005
X = -0.230217832 + -0.0005

Combine like terms: -0.230217832 + -0.0005 = -0.230717832
X = -0.230717832

Simplifying
X = -0.230717832


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.229717832, -0.230717832}

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