(x-0.3)(x-0.02)=0

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Solution for (x-0.3)(x-0.02)=0 equation: 


Simplifying
(x + -0.3)(x + -0.02) = 0

Reorder the terms:
(-0.3 + x)(x + -0.02) = 0

Reorder the terms:
(-0.3 + x)(-0.02 + x) = 0

Multiply (-0.3 + x) * (-0.02 + x)
(-0.3(-0.02 + x) + x(-0.02 + x)) = 0
((-0.02 * -0.3 + x * -0.3) + x(-0.02 + x)) = 0
((0.006 + -0.3x) + x(-0.02 + x)) = 0
(0.006 + -0.3x + (-0.02 * x + x * x)) = 0
(0.006 + -0.3x + (-0.02x + x2)) = 0

Combine like terms: -0.3x + -0.02x = -0.32x
(0.006 + -0.32x + x2) = 0

Solving
0.006 + -0.32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.006' to each side of the equation.
0.006 + -0.32x + -0.006 + x2 = 0 + -0.006

Reorder the terms:
0.006 + -0.006 + -0.32x + x2 = 0 + -0.006

Combine like terms: 0.006 + -0.006 = 0.000
0.000 + -0.32x + x2 = 0 + -0.006
-0.32x + x2 = 0 + -0.006

Combine like terms: 0 + -0.006 = -0.006
-0.32x + x2 = -0.006

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 = -0.006 + 0.0256

Reorder the terms:
0.0256 + -0.32x + x2 = -0.006 + 0.0256

Combine like terms: -0.006 + 0.0256 = 0.0196
0.0256 + -0.32x + x2 = 0.0196

Factor a perfect square on the left side:
(x + -0.16)(x + -0.16) = 0.0196

Calculate the square root of the right side: 0.14

Break this problem into two subproblems by setting 
(x + -0.16) equal to 0.14 and -0.14.


Subproblem 1
x + -0.16 = 0.14

Simplifying
x + -0.16 = 0.14

Reorder the terms:
-0.16 + x = 0.14

Solving
-0.16 + x = 0.14

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 = 0.14 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + x = 0.14 + 0.16
x = 0.14 + 0.16

Combine like terms: 0.14 + 0.16 = 0.3
x = 0.3

Simplifying
x = 0.3


Subproblem 2
x + -0.16 = -0.14

Simplifying
x + -0.16 = -0.14

Reorder the terms:
-0.16 + x = -0.14

Solving
-0.16 + x = -0.14

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 = -0.14 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + x = -0.14 + 0.16
x = -0.14 + 0.16

Combine like terms: -0.14 + 0.16 = 0.02
x = 0.02

Simplifying
x = 0.02


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3, 0.02}

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