(x+0.8)(x+1.7)=0

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Solution for (x+0.8)(x+1.7)=0 equation: 


Simplifying
(x + 0.8)(x + 1.7) = 0

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

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

Multiply (0.8 + x) * (1.7 + x)
(0.8(1.7 + x) + x(1.7 + x)) = 0
((1.7 * 0.8 + x * 0.8) + x(1.7 + x)) = 0
((1.36 + 0.8x) + x(1.7 + x)) = 0
(1.36 + 0.8x + (1.7 * x + x * x)) = 0
(1.36 + 0.8x + (1.7x + x2)) = 0

Combine like terms: 0.8x + 1.7x = 2.5x
(1.36 + 2.5x + x2) = 0

Solving
1.36 + 2.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.36' to each side of the equation.
1.36 + 2.5x + -1.36 + x2 = 0 + -1.36

Reorder the terms:
1.36 + -1.36 + 2.5x + x2 = 0 + -1.36

Combine like terms: 1.36 + -1.36 = 0.00
0.00 + 2.5x + x2 = 0 + -1.36
2.5x + x2 = 0 + -1.36

Combine like terms: 0 + -1.36 = -1.36
2.5x + x2 = -1.36

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -1.36 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -1.36 + 1.5625

Combine like terms: -1.36 + 1.5625 = 0.2025
1.5625 + 2.5x + x2 = 0.2025

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 0.2025

Calculate the square root of the right side: 0.45

Break this problem into two subproblems by setting 
(x + 1.25) equal to 0.45 and -0.45.


Subproblem 1
x + 1.25 = 0.45

Simplifying
x + 1.25 = 0.45

Reorder the terms:
1.25 + x = 0.45

Solving
1.25 + x = 0.45

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 0.45 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 0.45 + -1.25
x = 0.45 + -1.25

Combine like terms: 0.45 + -1.25 = -0.8
x = -0.8

Simplifying
x = -0.8


Subproblem 2
x + 1.25 = -0.45

Simplifying
x + 1.25 = -0.45

Reorder the terms:
1.25 + x = -0.45

Solving
1.25 + x = -0.45

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -0.45 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -0.45 + -1.25
x = -0.45 + -1.25

Combine like terms: -0.45 + -1.25 = -1.7
x = -1.7

Simplifying
x = -1.7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.8, -1.7}

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