(x+0.4)(x-0.1)=

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Solution for (x+0.4)(x-0.1)= equation: 


Simplifying
(x + 0.4)(x + -0.1) = 0

Reorder the terms:
(0.4 + x)(x + -0.1) = 0

Reorder the terms:
(0.4 + x)(-0.1 + x) = 0

Multiply (0.4 + x) * (-0.1 + x)
(0.4(-0.1 + x) + x(-0.1 + x)) = 0
((-0.1 * 0.4 + x * 0.4) + x(-0.1 + x)) = 0
((-0.04 + 0.4x) + x(-0.1 + x)) = 0
(-0.04 + 0.4x + (-0.1 * x + x * x)) = 0
(-0.04 + 0.4x + (-0.1x + x2)) = 0

Combine like terms: 0.4x + -0.1x = 0.3x
(-0.04 + 0.3x + x2) = 0

Solving
-0.04 + 0.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + 0.3x + 0.04 + x2 = 0 + 0.04

Reorder the terms:
-0.04 + 0.04 + 0.3x + x2 = 0 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + 0.3x + x2 = 0 + 0.04
0.3x + x2 = 0 + 0.04

Combine like terms: 0 + 0.04 = 0.04
0.3x + x2 = 0.04

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 0.04 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 0.04 + 0.0225

Combine like terms: 0.04 + 0.0225 = 0.0625
0.0225 + 0.3x + x2 = 0.0625

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(x + 0.15) equal to 0.25 and -0.25.


Subproblem 1
x + 0.15 = 0.25

Simplifying
x + 0.15 = 0.25

Reorder the terms:
0.15 + x = 0.25

Solving
0.15 + x = 0.25

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 0.25 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 0.25 + -0.15
x = 0.25 + -0.15

Combine like terms: 0.25 + -0.15 = 0.1
x = 0.1

Simplifying
x = 0.1


Subproblem 2
x + 0.15 = -0.25

Simplifying
x + 0.15 = -0.25

Reorder the terms:
0.15 + x = -0.25

Solving
0.15 + x = -0.25

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -0.25 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -0.25 + -0.15
x = -0.25 + -0.15

Combine like terms: -0.25 + -0.15 = -0.4
x = -0.4

Simplifying
x = -0.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1, -0.4}

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