x(0.09+x)=0.022

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Solution for x(0.09+x)=0.022 equation: 


Simplifying
x(0.09 + x) = 0.022
(0.09 * x + x * x) = 0.022
(0.09x + x2) = 0.022

Solving
0.09x + x2 = 0.022

Solving for variable 'x'.

Reorder the terms:
-0.022 + 0.09x + x2 = 0.022 + -0.022

Combine like terms: 0.022 + -0.022 = 0.000
-0.022 + 0.09x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.022' to each side of the equation.
-0.022 + 0.09x + 0.022 + x2 = 0.000 + 0.022

Reorder the terms:
-0.022 + 0.022 + 0.09x + x2 = 0.000 + 0.022

Combine like terms: -0.022 + 0.022 = 0.000
0.000 + 0.09x + x2 = 0.000 + 0.022
0.09x + x2 = 0.000 + 0.022

Combine like terms: 0.000 + 0.022 = 0.022
0.09x + x2 = 0.022

The x term is 0.09x.  Take half its coefficient (0.045).
Square it (0.002025) and add it to both sides.

Add '0.002025' to each side of the equation.
0.09x + 0.002025 + x2 = 0.022 + 0.002025

Reorder the terms:
0.002025 + 0.09x + x2 = 0.022 + 0.002025

Combine like terms: 0.022 + 0.002025 = 0.024025
0.002025 + 0.09x + x2 = 0.024025

Factor a perfect square on the left side:
(x + 0.045)(x + 0.045) = 0.024025

Calculate the square root of the right side: 0.155

Break this problem into two subproblems by setting 
(x + 0.045) equal to 0.155 and -0.155.


Subproblem 1
x + 0.045 = 0.155

Simplifying
x + 0.045 = 0.155

Reorder the terms:
0.045 + x = 0.155

Solving
0.045 + x = 0.155

Solving for variable 'x'.

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

Add '-0.045' to each side of the equation.
0.045 + -0.045 + x = 0.155 + -0.045

Combine like terms: 0.045 + -0.045 = 0.000
0.000 + x = 0.155 + -0.045
x = 0.155 + -0.045

Combine like terms: 0.155 + -0.045 = 0.11
x = 0.11

Simplifying
x = 0.11


Subproblem 2
x + 0.045 = -0.155

Simplifying
x + 0.045 = -0.155

Reorder the terms:
0.045 + x = -0.155

Solving
0.045 + x = -0.155

Solving for variable 'x'.

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

Add '-0.045' to each side of the equation.
0.045 + -0.045 + x = -0.155 + -0.045

Combine like terms: 0.045 + -0.045 = 0.000
0.000 + x = -0.155 + -0.045
x = -0.155 + -0.045

Combine like terms: -0.155 + -0.045 = -0.2
x = -0.2

Simplifying
x = -0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.11, -0.2}

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