-4.8x^2+16x+24=0

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Solution for -4.8x^2+16x+24=0 equation: 


Simplifying
-4.8x2 + 16x + 24 = 0

Reorder the terms:
24 + 16x + -4.8x2 = 0

Solving
24 + 16x + -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 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -3.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3.333333333x + x2 = 0 + 5
-3.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3.333333333x + x2 = 5

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 5 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 5 + 2.777777779

Combine like terms: 5 + 2.777777779 = 7.777777779
2.777777779 + -3.333333333x + x2 = 7.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 7.777777779

Calculate the square root of the right side: 2.788866755

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.788866755 and -2.788866755.


Subproblem 1
x + -1.666666667 = 2.788866755

Simplifying
x + -1.666666667 = 2.788866755

Reorder the terms:
-1.666666667 + x = 2.788866755

Solving
-1.666666667 + x = 2.788866755

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 2.788866755 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 2.788866755 + 1.666666667
x = 2.788866755 + 1.666666667

Combine like terms: 2.788866755 + 1.666666667 = 4.455533422
x = 4.455533422

Simplifying
x = 4.455533422


Subproblem 2
x + -1.666666667 = -2.788866755

Simplifying
x + -1.666666667 = -2.788866755

Reorder the terms:
-1.666666667 + x = -2.788866755

Solving
-1.666666667 + x = -2.788866755

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -2.788866755 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -2.788866755 + 1.666666667
x = -2.788866755 + 1.666666667

Combine like terms: -2.788866755 + 1.666666667 = -1.122200088
x = -1.122200088

Simplifying
x = -1.122200088


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.455533422, -1.122200088}

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