x^2+.000004x-.0000022=0

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Solution for x^2+.000004x-.0000022=0 equation:


Simplifying
x2 + 0.000004x + -0.0000022 = 0

Reorder the terms:
-0.0000022 + 0.000004x + x2 = 0

Solving
-0.0000022 + 0.000004x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0000022' to each side of the equation.
-0.0000022 + 0.000004x + 0.0000022 + x2 = 0 + 0.0000022

Reorder the terms:
-0.0000022 + 0.0000022 + 0.000004x + x2 = 0 + 0.0000022

Combine like terms: -0.0000022 + 0.0000022 = 0.0000000
0.0000000 + 0.000004x + x2 = 0 + 0.0000022
0.000004x + x2 = 0 + 0.0000022

Combine like terms: 0 + 0.0000022 = 0.0000022
0.000004x + x2 = 0.0000022

The x term is 0.000004x.  Take half its coefficient (0.000002).
Square it (0.000000000004) and add it to both sides.

Add '0.000000000004' to each side of the equation.
0.000004x + 0.000000000004 + x2 = 0.0000022 + 0.000000000004

Reorder the terms:
0.000000000004 + 0.000004x + x2 = 0.0000022 + 0.000000000004

Combine like terms: 0.0000022 + 0.000000000004 = 0.000002200004
0.000000000004 + 0.000004x + x2 = 0.000002200004

Factor a perfect square on the left side:
(x + 0.000002)(x + 0.000002) = 0.000002200004

Calculate the square root of the right side: 0.001483241

Break this problem into two subproblems by setting 
(x + 0.000002) equal to 0.001483241 and -0.001483241.

Subproblem 1

x + 0.000002 = 0.001483241 Simplifying x + 0.000002 = 0.001483241 Reorder the terms: 0.000002 + x = 0.001483241 Solving 0.000002 + x = 0.001483241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000002' to each side of the equation. 0.000002 + -0.000002 + x = 0.001483241 + -0.000002 Combine like terms: 0.000002 + -0.000002 = 0.000000 0.000000 + x = 0.001483241 + -0.000002 x = 0.001483241 + -0.000002 Combine like terms: 0.001483241 + -0.000002 = 0.001481241 x = 0.001481241 Simplifying x = 0.001481241

Subproblem 2

x + 0.000002 = -0.001483241 Simplifying x + 0.000002 = -0.001483241 Reorder the terms: 0.000002 + x = -0.001483241 Solving 0.000002 + x = -0.001483241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000002' to each side of the equation. 0.000002 + -0.000002 + x = -0.001483241 + -0.000002 Combine like terms: 0.000002 + -0.000002 = 0.000000 0.000000 + x = -0.001483241 + -0.000002 x = -0.001483241 + -0.000002 Combine like terms: -0.001483241 + -0.000002 = -0.001485241 x = -0.001485241 Simplifying x = -0.001485241

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.001481241, -0.001485241}

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