24x^2-96x+116=0

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Solution for 24x^2-96x+116=0 equation: 


Simplifying
24x2 + -96x + 116 = 0

Reorder the terms:
116 + -96x + 24x2 = 0

Solving
116 + -96x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(29 + -24x + 6x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(29 + -24x + 6x2)' equal to zero and attempt to solve:

Simplifying
29 + -24x + 6x2 = 0

Solving
29 + -24x + 6x2 = 0

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

Divide each side by '6'.
4.833333333 + -4x + x2 = 0

Move the constant term to the right:

Add '-4.833333333' to each side of the equation.
4.833333333 + -4x + -4.833333333 + x2 = 0 + -4.833333333

Reorder the terms:
4.833333333 + -4.833333333 + -4x + x2 = 0 + -4.833333333

Combine like terms: 4.833333333 + -4.833333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + -4.833333333
-4x + x2 = 0 + -4.833333333

Combine like terms: 0 + -4.833333333 = -4.833333333
-4x + x2 = -4.833333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -4.833333333 + 4

Reorder the terms:
4 + -4x + x2 = -4.833333333 + 4

Combine like terms: -4.833333333 + 4 = -0.833333333
4 + -4x + x2 = -0.833333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = -0.833333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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