(x+3.5)(x+5.6)=343

Solution for (x+3.5)(x+5.6)=343 equation:

Simplifying
(x + 3.5)(x + 5.6) = 343

Reorder the terms:
(3.5 + x)(x + 5.6) = 343

Reorder the terms:
(3.5 + x)(5.6 + x) = 343

Multiply (3.5 + x) * (5.6 + x)
(3.5(5.6 + x) + x(5.6 + x)) = 343
((5.6 * 3.5 + x * 3.5) + x(5.6 + x)) = 343
((19.6 + 3.5x) + x(5.6 + x)) = 343
(19.6 + 3.5x + (5.6 * x + x * x)) = 343
(19.6 + 3.5x + (5.6x + x2)) = 343

Combine like terms: 3.5x + 5.6x = 9.1x
(19.6 + 9.1x + x2) = 343

Solving
19.6 + 9.1x + x2 = 343

Solving for variable 'x'.

Reorder the terms:
19.6 + -343 + 9.1x + x2 = 343 + -343

Combine like terms: 19.6 + -343 = -323.4
-323.4 + 9.1x + x2 = 343 + -343

Combine like terms: 343 + -343 = 0
-323.4 + 9.1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '323.4' to each side of the equation.
-323.4 + 9.1x + 323.4 + x2 = 0 + 323.4

Reorder the terms:
-323.4 + 323.4 + 9.1x + x2 = 0 + 323.4

Combine like terms: -323.4 + 323.4 = 0.0
0.0 + 9.1x + x2 = 0 + 323.4
9.1x + x2 = 0 + 323.4

Combine like terms: 0 + 323.4 = 323.4
9.1x + x2 = 323.4

The x term is 9.1x.  Take half its coefficient (4.55).
Square it (20.7025) and add it to both sides.

Add '20.7025' to each side of the equation.
9.1x + 20.7025 + x2 = 323.4 + 20.7025

Reorder the terms:
20.7025 + 9.1x + x2 = 323.4 + 20.7025

Combine like terms: 323.4 + 20.7025 = 344.1025
20.7025 + 9.1x + x2 = 344.1025

Factor a perfect square on the left side:
(x + 4.55)(x + 4.55) = 344.1025

Calculate the square root of the right side: 18.55

Break this problem into two subproblems by setting 
(x + 4.55) equal to 18.55 and -18.55.

Subproblem 1
x + 4.55 = 18.55

Simplifying
x + 4.55 = 18.55

Reorder the terms:
4.55 + x = 18.55

Solving
4.55 + x = 18.55

Solving for variable 'x'.

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

Add '-4.55' to each side of the equation.
4.55 + -4.55 + x = 18.55 + -4.55

Combine like terms: 4.55 + -4.55 = 0.00
0.00 + x = 18.55 + -4.55
x = 18.55 + -4.55

Combine like terms: 18.55 + -4.55 = 14
x = 14

Simplifying
x = 14

Subproblem 2
x + 4.55 = -18.55

Simplifying
x + 4.55 = -18.55

Reorder the terms:
4.55 + x = -18.55

Solving
4.55 + x = -18.55

Solving for variable 'x'.

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

Add '-4.55' to each side of the equation.
4.55 + -4.55 + x = -18.55 + -4.55

Combine like terms: 4.55 + -4.55 = 0.00
0.00 + x = -18.55 + -4.55
x = -18.55 + -4.55

Combine like terms: -18.55 + -4.55 = -23.1
x = -23.1

Simplifying
x = -23.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14, -23.1}