(x-5.6)(x+4.5)=

Solution for (x-5.6)(x+4.5)= equation:

Simplifying
(x + -5.6)(x + 4.5) = 0

Reorder the terms:
(-5.6 + x)(x + 4.5) = 0

Reorder the terms:
(-5.6 + x)(4.5 + x) = 0

Multiply (-5.6 + x) * (4.5 + x)
(-5.6(4.5 + x) + x(4.5 + x)) = 0
((4.5 * -5.6 + x * -5.6) + x(4.5 + x)) = 0
((-25.2 + -5.6x) + x(4.5 + x)) = 0
(-25.2 + -5.6x + (4.5 * x + x * x)) = 0
(-25.2 + -5.6x + (4.5x + x2)) = 0

Combine like terms: -5.6x + 4.5x = -1.1x
(-25.2 + -1.1x + x2) = 0

Solving
-25.2 + -1.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '25.2' to each side of the equation.
-25.2 + -1.1x + 25.2 + x2 = 0 + 25.2

Reorder the terms:
-25.2 + 25.2 + -1.1x + x2 = 0 + 25.2

Combine like terms: -25.2 + 25.2 = 0.0
0.0 + -1.1x + x2 = 0 + 25.2
-1.1x + x2 = 0 + 25.2

Combine like terms: 0 + 25.2 = 25.2
-1.1x + x2 = 25.2

The x term is -1.1x.  Take half its coefficient (-0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
-1.1x + 0.3025 + x2 = 25.2 + 0.3025

Reorder the terms:
0.3025 + -1.1x + x2 = 25.2 + 0.3025

Combine like terms: 25.2 + 0.3025 = 25.5025
0.3025 + -1.1x + x2 = 25.5025

Factor a perfect square on the left side:
(x + -0.55)(x + -0.55) = 25.5025

Calculate the square root of the right side: 5.05

Break this problem into two subproblems by setting 
(x + -0.55) equal to 5.05 and -5.05.

Subproblem 1
x + -0.55 = 5.05

Simplifying
x + -0.55 = 5.05

Reorder the terms:
-0.55 + x = 5.05

Solving
-0.55 + x = 5.05

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = 5.05 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = 5.05 + 0.55
x = 5.05 + 0.55

Combine like terms: 5.05 + 0.55 = 5.6
x = 5.6

Simplifying
x = 5.6

Subproblem 2
x + -0.55 = -5.05

Simplifying
x + -0.55 = -5.05

Reorder the terms:
-0.55 + x = -5.05

Solving
-0.55 + x = -5.05

Solving for variable 'x'.

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

Add '0.55' to each side of the equation.
-0.55 + 0.55 + x = -5.05 + 0.55

Combine like terms: -0.55 + 0.55 = 0.00
0.00 + x = -5.05 + 0.55
x = -5.05 + 0.55

Combine like terms: -5.05 + 0.55 = -4.5
x = -4.5

Simplifying
x = -4.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.6, -4.5}