48(x^2)-78(x)+33=0

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Solution for 48(x^2)-78(x)+33=0 equation: 


Simplifying
48(x2) + -78(x) + 33 = 0

Reorder the terms:
33 + -78x + 48x2 = 0

Solving
33 + -78x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(11 + -26x + 16x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(11 + -26x + 16x2)' equal to zero and attempt to solve:

Simplifying
11 + -26x + 16x2 = 0

Solving
11 + -26x + 16x2 = 0

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

Divide each side by '16'.
0.6875 + -1.625x + x2 = 0

Move the constant term to the right:

Add '-0.6875' to each side of the equation.
0.6875 + -1.625x + -0.6875 + x2 = 0 + -0.6875

Reorder the terms:
0.6875 + -0.6875 + -1.625x + x2 = 0 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + -1.625x + x2 = 0 + -0.6875
-1.625x + x2 = 0 + -0.6875

Combine like terms: 0 + -0.6875 = -0.6875
-1.625x + x2 = -0.6875

The x term is -1.625x.  Take half its coefficient (-0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
-1.625x + 0.66015625 + x2 = -0.6875 + 0.66015625

Reorder the terms:
0.66015625 + -1.625x + x2 = -0.6875 + 0.66015625

Combine like terms: -0.6875 + 0.66015625 = -0.02734375
0.66015625 + -1.625x + x2 = -0.02734375

Factor a perfect square on the left side:
(x + -0.8125)(x + -0.8125) = -0.02734375

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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