(0.20+x)(0.12+x)=

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Solution for (0.20+x)(0.12+x)= equation: 


Simplifying
(0.20 + x)(0.12 + x) = 0

Multiply (0.20 + x) * (0.12 + x)
(0.20(0.12 + x) + x(0.12 + x)) = 0
((0.12 * 0.20 + x * 0.20) + x(0.12 + x)) = 0
((0.024 + 0.20x) + x(0.12 + x)) = 0
(0.024 + 0.20x + (0.12 * x + x * x)) = 0
(0.024 + 0.20x + (0.12x + x2)) = 0

Combine like terms: 0.20x + 0.12x = 0.32x
(0.024 + 0.32x + x2) = 0

Solving
0.024 + 0.32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.024' to each side of the equation.
0.024 + 0.32x + -0.024 + x2 = 0 + -0.024

Reorder the terms:
0.024 + -0.024 + 0.32x + x2 = 0 + -0.024

Combine like terms: 0.024 + -0.024 = 0.000
0.000 + 0.32x + x2 = 0 + -0.024
0.32x + x2 = 0 + -0.024

Combine like terms: 0 + -0.024 = -0.024
0.32x + x2 = -0.024

The x term is 0.32x.  Take half its coefficient (0.16).
Square it (0.0256) and add it to both sides.

Add '0.0256' to each side of the equation.
0.32x + 0.0256 + x2 = -0.024 + 0.0256

Reorder the terms:
0.0256 + 0.32x + x2 = -0.024 + 0.0256

Combine like terms: -0.024 + 0.0256 = 0.0016
0.0256 + 0.32x + x2 = 0.0016

Factor a perfect square on the left side:
(x + 0.16)(x + 0.16) = 0.0016

Calculate the square root of the right side: 0.04

Break this problem into two subproblems by setting 
(x + 0.16) equal to 0.04 and -0.04.


Subproblem 1
x + 0.16 = 0.04

Simplifying
x + 0.16 = 0.04

Reorder the terms:
0.16 + x = 0.04

Solving
0.16 + x = 0.04

Solving for variable 'x'.

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

Add '-0.16' to each side of the equation.
0.16 + -0.16 + x = 0.04 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + x = 0.04 + -0.16
x = 0.04 + -0.16

Combine like terms: 0.04 + -0.16 = -0.12
x = -0.12

Simplifying
x = -0.12


Subproblem 2
x + 0.16 = -0.04

Simplifying
x + 0.16 = -0.04

Reorder the terms:
0.16 + x = -0.04

Solving
0.16 + x = -0.04

Solving for variable 'x'.

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

Add '-0.16' to each side of the equation.
0.16 + -0.16 + x = -0.04 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + x = -0.04 + -0.16
x = -0.04 + -0.16

Combine like terms: -0.04 + -0.16 = -0.2
x = -0.2

Simplifying
x = -0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.12, -0.2}

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