(x+0.5)(x+4.8)=0

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Solution for (x+0.5)(x+4.8)=0 equation: 


Simplifying
(x + 0.5)(x + 4.8) = 0

Reorder the terms:
(0.5 + x)(x + 4.8) = 0

Reorder the terms:
(0.5 + x)(4.8 + x) = 0

Multiply (0.5 + x) * (4.8 + x)
(0.5(4.8 + x) + x(4.8 + x)) = 0
((4.8 * 0.5 + x * 0.5) + x(4.8 + x)) = 0
((2.4 + 0.5x) + x(4.8 + x)) = 0
(2.4 + 0.5x + (4.8 * x + x * x)) = 0
(2.4 + 0.5x + (4.8x + x2)) = 0

Combine like terms: 0.5x + 4.8x = 5.3x
(2.4 + 5.3x + x2) = 0

Solving
2.4 + 5.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + 5.3x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + 5.3x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + 5.3x + x2 = 0 + -2.4
5.3x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
5.3x + x2 = -2.4

The x term is 5.3x.  Take half its coefficient (2.65).
Square it (7.0225) and add it to both sides.

Add '7.0225' to each side of the equation.
5.3x + 7.0225 + x2 = -2.4 + 7.0225

Reorder the terms:
7.0225 + 5.3x + x2 = -2.4 + 7.0225

Combine like terms: -2.4 + 7.0225 = 4.6225
7.0225 + 5.3x + x2 = 4.6225

Factor a perfect square on the left side:
(x + 2.65)(x + 2.65) = 4.6225

Calculate the square root of the right side: 2.15

Break this problem into two subproblems by setting 
(x + 2.65) equal to 2.15 and -2.15.


Subproblem 1
x + 2.65 = 2.15

Simplifying
x + 2.65 = 2.15

Reorder the terms:
2.65 + x = 2.15

Solving
2.65 + x = 2.15

Solving for variable 'x'.

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

Add '-2.65' to each side of the equation.
2.65 + -2.65 + x = 2.15 + -2.65

Combine like terms: 2.65 + -2.65 = 0.00
0.00 + x = 2.15 + -2.65
x = 2.15 + -2.65

Combine like terms: 2.15 + -2.65 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 2.65 = -2.15

Simplifying
x + 2.65 = -2.15

Reorder the terms:
2.65 + x = -2.15

Solving
2.65 + x = -2.15

Solving for variable 'x'.

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

Add '-2.65' to each side of the equation.
2.65 + -2.65 + x = -2.15 + -2.65

Combine like terms: 2.65 + -2.65 = 0.00
0.00 + x = -2.15 + -2.65
x = -2.15 + -2.65

Combine like terms: -2.15 + -2.65 = -4.8
x = -4.8

Simplifying
x = -4.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -4.8}

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