-48x^2+1.6x+24=0

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Solution for -48x^2+1.6x+24=0 equation: 


Simplifying
-48x2 + 1.6x + 24 = 0

Reorder the terms:
24 + 1.6x + -48x2 = 0

Solving
24 + 1.6x + -48x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
-0.5 + -0.03333333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.03333333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.03333333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.03333333333x + x2 = 0 + 0.5
-0.03333333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.03333333333x + x2 = 0.5

The x term is -0.03333333333x.  Take half its coefficient (-0.01666666667).
Square it (0.0002777777779) and add it to both sides.

Add '0.0002777777779' to each side of the equation.
-0.03333333333x + 0.0002777777779 + x2 = 0.5 + 0.0002777777779

Reorder the terms:
0.0002777777779 + -0.03333333333x + x2 = 0.5 + 0.0002777777779

Combine like terms: 0.5 + 0.0002777777779 = 0.5002777777779
0.0002777777779 + -0.03333333333x + x2 = 0.5002777777779

Factor a perfect square on the left side:
(x + -0.01666666667)(x + -0.01666666667) = 0.5002777777779

Calculate the square root of the right side: 0.707303172

Break this problem into two subproblems by setting 
(x + -0.01666666667) equal to 0.707303172 and -0.707303172.


Subproblem 1
x + -0.01666666667 = 0.707303172

Simplifying
x + -0.01666666667 = 0.707303172

Reorder the terms:
-0.01666666667 + x = 0.707303172

Solving
-0.01666666667 + x = 0.707303172

Solving for variable 'x'.

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

Add '0.01666666667' to each side of the equation.
-0.01666666667 + 0.01666666667 + x = 0.707303172 + 0.01666666667

Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000
0.00000000000 + x = 0.707303172 + 0.01666666667
x = 0.707303172 + 0.01666666667

Combine like terms: 0.707303172 + 0.01666666667 = 0.72396983867
x = 0.72396983867

Simplifying
x = 0.72396983867


Subproblem 2
x + -0.01666666667 = -0.707303172

Simplifying
x + -0.01666666667 = -0.707303172

Reorder the terms:
-0.01666666667 + x = -0.707303172

Solving
-0.01666666667 + x = -0.707303172

Solving for variable 'x'.

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

Add '0.01666666667' to each side of the equation.
-0.01666666667 + 0.01666666667 + x = -0.707303172 + 0.01666666667

Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000
0.00000000000 + x = -0.707303172 + 0.01666666667
x = -0.707303172 + 0.01666666667

Combine like terms: -0.707303172 + 0.01666666667 = -0.69063650533
x = -0.69063650533

Simplifying
x = -0.69063650533


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.72396983867, -0.69063650533}

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