(x+0.5)(x+3.4)=0

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Solution for (x+0.5)(x+3.4)=0 equation: 


Simplifying
(x + 0.5)(x + 3.4) = 0

Reorder the terms:
(0.5 + x)(x + 3.4) = 0

Reorder the terms:
(0.5 + x)(3.4 + x) = 0

Multiply (0.5 + x) * (3.4 + x)
(0.5(3.4 + x) + x(3.4 + x)) = 0
((3.4 * 0.5 + x * 0.5) + x(3.4 + x)) = 0
((1.7 + 0.5x) + x(3.4 + x)) = 0
(1.7 + 0.5x + (3.4 * x + x * x)) = 0
(1.7 + 0.5x + (3.4x + x2)) = 0

Combine like terms: 0.5x + 3.4x = 3.9x
(1.7 + 3.9x + x2) = 0

Solving
1.7 + 3.9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.7' to each side of the equation.
1.7 + 3.9x + -1.7 + x2 = 0 + -1.7

Reorder the terms:
1.7 + -1.7 + 3.9x + x2 = 0 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + 3.9x + x2 = 0 + -1.7
3.9x + x2 = 0 + -1.7

Combine like terms: 0 + -1.7 = -1.7
3.9x + x2 = -1.7

The x term is 3.9x.  Take half its coefficient (1.95).
Square it (3.8025) and add it to both sides.

Add '3.8025' to each side of the equation.
3.9x + 3.8025 + x2 = -1.7 + 3.8025

Reorder the terms:
3.8025 + 3.9x + x2 = -1.7 + 3.8025

Combine like terms: -1.7 + 3.8025 = 2.1025
3.8025 + 3.9x + x2 = 2.1025

Factor a perfect square on the left side:
(x + 1.95)(x + 1.95) = 2.1025

Calculate the square root of the right side: 1.45

Break this problem into two subproblems by setting 
(x + 1.95) equal to 1.45 and -1.45.


Subproblem 1
x + 1.95 = 1.45

Simplifying
x + 1.95 = 1.45

Reorder the terms:
1.95 + x = 1.45

Solving
1.95 + x = 1.45

Solving for variable 'x'.

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

Add '-1.95' to each side of the equation.
1.95 + -1.95 + x = 1.45 + -1.95

Combine like terms: 1.95 + -1.95 = 0.00
0.00 + x = 1.45 + -1.95
x = 1.45 + -1.95

Combine like terms: 1.45 + -1.95 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 1.95 = -1.45

Simplifying
x + 1.95 = -1.45

Reorder the terms:
1.95 + x = -1.45

Solving
1.95 + x = -1.45

Solving for variable 'x'.

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

Add '-1.95' to each side of the equation.
1.95 + -1.95 + x = -1.45 + -1.95

Combine like terms: 1.95 + -1.95 = 0.00
0.00 + x = -1.45 + -1.95
x = -1.45 + -1.95

Combine like terms: -1.45 + -1.95 = -3.4
x = -3.4

Simplifying
x = -3.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -3.4}

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