x^2-4.8x-19.2=0

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Solution for x^2-4.8x-19.2=0 equation: 


Simplifying
x2 + -4.8x + -19.2 = 0

Reorder the terms:
-19.2 + -4.8x + x2 = 0

Solving
-19.2 + -4.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '19.2' to each side of the equation.
-19.2 + -4.8x + 19.2 + x2 = 0 + 19.2

Reorder the terms:
-19.2 + 19.2 + -4.8x + x2 = 0 + 19.2

Combine like terms: -19.2 + 19.2 = 0.0
0.0 + -4.8x + x2 = 0 + 19.2
-4.8x + x2 = 0 + 19.2

Combine like terms: 0 + 19.2 = 19.2
-4.8x + x2 = 19.2

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = 19.2 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = 19.2 + 5.76

Combine like terms: 19.2 + 5.76 = 24.96
5.76 + -4.8x + x2 = 24.96

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 24.96

Calculate the square root of the right side: 4.995998399

Break this problem into two subproblems by setting 
(x + -2.4) equal to 4.995998399 and -4.995998399.


Subproblem 1
x + -2.4 = 4.995998399

Simplifying
x + -2.4 = 4.995998399

Reorder the terms:
-2.4 + x = 4.995998399

Solving
-2.4 + x = 4.995998399

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = 4.995998399 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 4.995998399 + 2.4
x = 4.995998399 + 2.4

Combine like terms: 4.995998399 + 2.4 = 7.395998399
x = 7.395998399

Simplifying
x = 7.395998399


Subproblem 2
x + -2.4 = -4.995998399

Simplifying
x + -2.4 = -4.995998399

Reorder the terms:
-2.4 + x = -4.995998399

Solving
-2.4 + x = -4.995998399

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = -4.995998399 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -4.995998399 + 2.4
x = -4.995998399 + 2.4

Combine like terms: -4.995998399 + 2.4 = -2.595998399
x = -2.595998399

Simplifying
x = -2.595998399


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.395998399, -2.595998399}

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