-4.8x^2+1.6x+24=0

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Solution for -4.8x^2+1.6x+24=0 equation: 


Simplifying
-4.8x2 + 1.6x + 24 = 0

Reorder the terms:
24 + 1.6x + -4.8x2 = 0

Solving
24 + 1.6x + -4.8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.8 the coefficient of the squared term: 

Divide each side by '-4.8'.
-5 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.3333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.3333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.3333333333x + x2 = 0 + 5
-0.3333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.3333333333x + x2 = 5

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 5 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 5 + 0.02777777779

Combine like terms: 5 + 0.02777777779 = 5.02777777779
0.02777777779 + -0.3333333333x + x2 = 5.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 5.02777777779

Calculate the square root of the right side: 2.242270675

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 2.242270675 and -2.242270675.


Subproblem 1
x + -0.1666666667 = 2.242270675

Simplifying
x + -0.1666666667 = 2.242270675

Reorder the terms:
-0.1666666667 + x = 2.242270675

Solving
-0.1666666667 + x = 2.242270675

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 2.242270675 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 2.242270675 + 0.1666666667
x = 2.242270675 + 0.1666666667

Combine like terms: 2.242270675 + 0.1666666667 = 2.4089373417
x = 2.4089373417

Simplifying
x = 2.4089373417


Subproblem 2
x + -0.1666666667 = -2.242270675

Simplifying
x + -0.1666666667 = -2.242270675

Reorder the terms:
-0.1666666667 + x = -2.242270675

Solving
-0.1666666667 + x = -2.242270675

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -2.242270675 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -2.242270675 + 0.1666666667
x = -2.242270675 + 0.1666666667

Combine like terms: -2.242270675 + 0.1666666667 = -2.0756040083
x = -2.0756040083

Simplifying
x = -2.0756040083


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4089373417, -2.0756040083}

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