x(x+0.16)=0.042

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Solution for x(x+0.16)=0.042 equation: 


Simplifying
x(x + 0.16) = 0.042

Reorder the terms:
x(0.16 + x) = 0.042
(0.16 * x + x * x) = 0.042
(0.16x + x2) = 0.042

Solving
0.16x + x2 = 0.042

Solving for variable 'x'.

Reorder the terms:
-0.042 + 0.16x + x2 = 0.042 + -0.042

Combine like terms: 0.042 + -0.042 = 0.000
-0.042 + 0.16x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.042' to each side of the equation.
-0.042 + 0.16x + 0.042 + x2 = 0.000 + 0.042

Reorder the terms:
-0.042 + 0.042 + 0.16x + x2 = 0.000 + 0.042

Combine like terms: -0.042 + 0.042 = 0.000
0.000 + 0.16x + x2 = 0.000 + 0.042
0.16x + x2 = 0.000 + 0.042

Combine like terms: 0.000 + 0.042 = 0.042
0.16x + x2 = 0.042

The x term is 0.16x.  Take half its coefficient (0.08).
Square it (0.0064) and add it to both sides.

Add '0.0064' to each side of the equation.
0.16x + 0.0064 + x2 = 0.042 + 0.0064

Reorder the terms:
0.0064 + 0.16x + x2 = 0.042 + 0.0064

Combine like terms: 0.042 + 0.0064 = 0.0484
0.0064 + 0.16x + x2 = 0.0484

Factor a perfect square on the left side:
(x + 0.08)(x + 0.08) = 0.0484

Calculate the square root of the right side: 0.22

Break this problem into two subproblems by setting 
(x + 0.08) equal to 0.22 and -0.22.


Subproblem 1
x + 0.08 = 0.22

Simplifying
x + 0.08 = 0.22

Reorder the terms:
0.08 + x = 0.22

Solving
0.08 + x = 0.22

Solving for variable 'x'.

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

Add '-0.08' to each side of the equation.
0.08 + -0.08 + x = 0.22 + -0.08

Combine like terms: 0.08 + -0.08 = 0.00
0.00 + x = 0.22 + -0.08
x = 0.22 + -0.08

Combine like terms: 0.22 + -0.08 = 0.14
x = 0.14

Simplifying
x = 0.14


Subproblem 2
x + 0.08 = -0.22

Simplifying
x + 0.08 = -0.22

Reorder the terms:
0.08 + x = -0.22

Solving
0.08 + x = -0.22

Solving for variable 'x'.

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

Add '-0.08' to each side of the equation.
0.08 + -0.08 + x = -0.22 + -0.08

Combine like terms: 0.08 + -0.08 = 0.00
0.00 + x = -0.22 + -0.08
x = -0.22 + -0.08

Combine like terms: -0.22 + -0.08 = -0.3
x = -0.3

Simplifying
x = -0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.14, -0.3}

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