.000022-.00044x=x^2

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Solution for .000022-.00044x=x^2 equation:


Simplifying
0.000022 + -0.00044x = x2

Solving
0.000022 + -0.00044x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
0.000022 + -0.00044x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.000022 + 0.00044x + x2 = 0

Move the constant term to the right:

Add '0.000022' to each side of the equation.
-0.000022 + 0.00044x + 0.000022 + x2 = 0 + 0.000022

Reorder the terms:
-0.000022 + 0.000022 + 0.00044x + x2 = 0 + 0.000022

Combine like terms: -0.000022 + 0.000022 = 0.000000
0.000000 + 0.00044x + x2 = 0 + 0.000022
0.00044x + x2 = 0 + 0.000022

Combine like terms: 0 + 0.000022 = 0.000022
0.00044x + x2 = 0.000022

The x term is 0.00044x.  Take half its coefficient (0.00022).
Square it (0.0000000484) and add it to both sides.

Add '0.0000000484' to each side of the equation.
0.00044x + 0.0000000484 + x2 = 0.000022 + 0.0000000484

Reorder the terms:
0.0000000484 + 0.00044x + x2 = 0.000022 + 0.0000000484

Combine like terms: 0.000022 + 0.0000000484 = 0.0000220484
0.0000000484 + 0.00044x + x2 = 0.0000220484

Factor a perfect square on the left side:
(x + 0.00022)(x + 0.00022) = 0.0000220484

Calculate the square root of the right side: 0.004695572

Break this problem into two subproblems by setting 
(x + 0.00022) equal to 0.004695572 and -0.004695572.

Subproblem 1

x + 0.00022 = 0.004695572 Simplifying x + 0.00022 = 0.004695572 Reorder the terms: 0.00022 + x = 0.004695572 Solving 0.00022 + x = 0.004695572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00022' to each side of the equation. 0.00022 + -0.00022 + x = 0.004695572 + -0.00022 Combine like terms: 0.00022 + -0.00022 = 0.00000 0.00000 + x = 0.004695572 + -0.00022 x = 0.004695572 + -0.00022 Combine like terms: 0.004695572 + -0.00022 = 0.004475572 x = 0.004475572 Simplifying x = 0.004475572

Subproblem 2

x + 0.00022 = -0.004695572 Simplifying x + 0.00022 = -0.004695572 Reorder the terms: 0.00022 + x = -0.004695572 Solving 0.00022 + x = -0.004695572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00022' to each side of the equation. 0.00022 + -0.00022 + x = -0.004695572 + -0.00022 Combine like terms: 0.00022 + -0.00022 = 0.00000 0.00000 + x = -0.004695572 + -0.00022 x = -0.004695572 + -0.00022 Combine like terms: -0.004695572 + -0.00022 = -0.004915572 x = -0.004915572 Simplifying x = -0.004915572

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.004475572, -0.004915572}

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