X^2+0.001X-0.001=0

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


Simplifying
X2 + 0.001X + -0.001 = 0

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

Solving
-0.001 + 0.001X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 0.001 + 0.00000025

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

Combine like terms: 0.001 + 0.00000025 = 0.00100025
0.00000025 + 0.001X + X2 = 0.00100025

Factor a perfect square on the left side:
(X + 0.0005)(X + 0.0005) = 0.00100025

Calculate the square root of the right side: 0.031626729

Break this problem into two subproblems by setting 
(X + 0.0005) equal to 0.031626729 and -0.031626729.

Subproblem 1

X + 0.0005 = 0.031626729 Simplifying X + 0.0005 = 0.031626729 Reorder the terms: 0.0005 + X = 0.031626729 Solving 0.0005 + X = 0.031626729 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 = 0.031626729 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = 0.031626729 + -0.0005 X = 0.031626729 + -0.0005 Combine like terms: 0.031626729 + -0.0005 = 0.031126729 X = 0.031126729 Simplifying X = 0.031126729

Subproblem 2

X + 0.0005 = -0.031626729 Simplifying X + 0.0005 = -0.031626729 Reorder the terms: 0.0005 + X = -0.031626729 Solving 0.0005 + X = -0.031626729 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 = -0.031626729 + -0.0005 Combine like terms: 0.0005 + -0.0005 = 0.0000 0.0000 + X = -0.031626729 + -0.0005 X = -0.031626729 + -0.0005 Combine like terms: -0.031626729 + -0.0005 = -0.032126729 X = -0.032126729 Simplifying X = -0.032126729

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.031126729, -0.032126729}

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