-0.24x^2+3.2x+60=0

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Solution for -0.24x^2+3.2x+60=0 equation: 


Simplifying
-0.24x2 + 3.2x + 60 = 0

Reorder the terms:
60 + 3.2x + -0.24x2 = 0

Solving
60 + 3.2x + -0.24x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.24 the coefficient of the squared term: 

Divide each side by '-0.24'.
-250 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + -13.33333333x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + -13.33333333x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + -13.33333333x + x2 = 0 + 250
-13.33333333x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
-13.33333333x + x2 = 250

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = 250 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = 250 + 44.44444442

Combine like terms: 250 + 44.44444442 = 294.44444442
44.44444442 + -13.33333333x + x2 = 294.44444442

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 294.44444442

Calculate the square root of the right side: 17.159383568

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 17.159383568 and -17.159383568.


Subproblem 1
x + -6.666666665 = 17.159383568

Simplifying
x + -6.666666665 = 17.159383568

Reorder the terms:
-6.666666665 + x = 17.159383568

Solving
-6.666666665 + x = 17.159383568

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 17.159383568 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 17.159383568 + 6.666666665
x = 17.159383568 + 6.666666665

Combine like terms: 17.159383568 + 6.666666665 = 23.826050233
x = 23.826050233

Simplifying
x = 23.826050233


Subproblem 2
x + -6.666666665 = -17.159383568

Simplifying
x + -6.666666665 = -17.159383568

Reorder the terms:
-6.666666665 + x = -17.159383568

Solving
-6.666666665 + x = -17.159383568

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -17.159383568 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -17.159383568 + 6.666666665
x = -17.159383568 + 6.666666665

Combine like terms: -17.159383568 + 6.666666665 = -10.492716903
x = -10.492716903

Simplifying
x = -10.492716903


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.826050233, -10.492716903}

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