(x+0.4)(x+1.7)=0

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Solution for (x+0.4)(x+1.7)=0 equation: 


Simplifying
(x + 0.4)(x + 1.7) = 0

Reorder the terms:
(0.4 + x)(x + 1.7) = 0

Reorder the terms:
(0.4 + x)(1.7 + x) = 0

Multiply (0.4 + x) * (1.7 + x)
(0.4(1.7 + x) + x(1.7 + x)) = 0
((1.7 * 0.4 + x * 0.4) + x(1.7 + x)) = 0
((0.68 + 0.4x) + x(1.7 + x)) = 0
(0.68 + 0.4x + (1.7 * x + x * x)) = 0
(0.68 + 0.4x + (1.7x + x2)) = 0

Combine like terms: 0.4x + 1.7x = 2.1x
(0.68 + 2.1x + x2) = 0

Solving
0.68 + 2.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.68' to each side of the equation.
0.68 + 2.1x + -0.68 + x2 = 0 + -0.68

Reorder the terms:
0.68 + -0.68 + 2.1x + x2 = 0 + -0.68

Combine like terms: 0.68 + -0.68 = 0.00
0.00 + 2.1x + x2 = 0 + -0.68
2.1x + x2 = 0 + -0.68

Combine like terms: 0 + -0.68 = -0.68
2.1x + x2 = -0.68

The x term is 2.1x.  Take half its coefficient (1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
2.1x + 1.1025 + x2 = -0.68 + 1.1025

Reorder the terms:
1.1025 + 2.1x + x2 = -0.68 + 1.1025

Combine like terms: -0.68 + 1.1025 = 0.4225
1.1025 + 2.1x + x2 = 0.4225

Factor a perfect square on the left side:
(x + 1.05)(x + 1.05) = 0.4225

Calculate the square root of the right side: 0.65

Break this problem into two subproblems by setting 
(x + 1.05) equal to 0.65 and -0.65.


Subproblem 1
x + 1.05 = 0.65

Simplifying
x + 1.05 = 0.65

Reorder the terms:
1.05 + x = 0.65

Solving
1.05 + x = 0.65

Solving for variable 'x'.

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

Add '-1.05' to each side of the equation.
1.05 + -1.05 + x = 0.65 + -1.05

Combine like terms: 1.05 + -1.05 = 0.00
0.00 + x = 0.65 + -1.05
x = 0.65 + -1.05

Combine like terms: 0.65 + -1.05 = -0.4
x = -0.4

Simplifying
x = -0.4


Subproblem 2
x + 1.05 = -0.65

Simplifying
x + 1.05 = -0.65

Reorder the terms:
1.05 + x = -0.65

Solving
1.05 + x = -0.65

Solving for variable 'x'.

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

Add '-1.05' to each side of the equation.
1.05 + -1.05 + x = -0.65 + -1.05

Combine like terms: 1.05 + -1.05 = 0.00
0.00 + x = -0.65 + -1.05
x = -0.65 + -1.05

Combine like terms: -0.65 + -1.05 = -1.7
x = -1.7

Simplifying
x = -1.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.4, -1.7}

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