(x-4.5)(x+3.2)=0

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Solution for (x-4.5)(x+3.2)=0 equation: 


Simplifying
(x + -4.5)(x + 3.2) = 0

Reorder the terms:
(-4.5 + x)(x + 3.2) = 0

Reorder the terms:
(-4.5 + x)(3.2 + x) = 0

Multiply (-4.5 + x) * (3.2 + x)
(-4.5(3.2 + x) + x(3.2 + x)) = 0
((3.2 * -4.5 + x * -4.5) + x(3.2 + x)) = 0
((-14.4 + -4.5x) + x(3.2 + x)) = 0
(-14.4 + -4.5x + (3.2 * x + x * x)) = 0
(-14.4 + -4.5x + (3.2x + x2)) = 0

Combine like terms: -4.5x + 3.2x = -1.3x
(-14.4 + -1.3x + x2) = 0

Solving
-14.4 + -1.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '14.4' to each side of the equation.
-14.4 + -1.3x + 14.4 + x2 = 0 + 14.4

Reorder the terms:
-14.4 + 14.4 + -1.3x + x2 = 0 + 14.4

Combine like terms: -14.4 + 14.4 = 0.0
0.0 + -1.3x + x2 = 0 + 14.4
-1.3x + x2 = 0 + 14.4

Combine like terms: 0 + 14.4 = 14.4
-1.3x + x2 = 14.4

The x term is -1.3x.  Take half its coefficient (-0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
-1.3x + 0.4225 + x2 = 14.4 + 0.4225

Reorder the terms:
0.4225 + -1.3x + x2 = 14.4 + 0.4225

Combine like terms: 14.4 + 0.4225 = 14.8225
0.4225 + -1.3x + x2 = 14.8225

Factor a perfect square on the left side:
(x + -0.65)(x + -0.65) = 14.8225

Calculate the square root of the right side: 3.85

Break this problem into two subproblems by setting 
(x + -0.65) equal to 3.85 and -3.85.


Subproblem 1
x + -0.65 = 3.85

Simplifying
x + -0.65 = 3.85

Reorder the terms:
-0.65 + x = 3.85

Solving
-0.65 + x = 3.85

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x = 3.85 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x = 3.85 + 0.65
x = 3.85 + 0.65

Combine like terms: 3.85 + 0.65 = 4.5
x = 4.5

Simplifying
x = 4.5


Subproblem 2
x + -0.65 = -3.85

Simplifying
x + -0.65 = -3.85

Reorder the terms:
-0.65 + x = -3.85

Solving
-0.65 + x = -3.85

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x = -3.85 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x = -3.85 + 0.65
x = -3.85 + 0.65

Combine like terms: -3.85 + 0.65 = -3.2
x = -3.2

Simplifying
x = -3.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5, -3.2}

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