16x^2-68x+78=0

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Solution for 16x^2-68x+78=0 equation: 


Simplifying
16x2 + -68x + 78 = 0

Reorder the terms:
78 + -68x + 16x2 = 0

Solving
78 + -68x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(39 + -34x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(39 + -34x + 8x2)' equal to zero and attempt to solve:

Simplifying
39 + -34x + 8x2 = 0

Solving
39 + -34x + 8x2 = 0

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

Divide each side by '8'.
4.875 + -4.25x + x2 = 0

Move the constant term to the right:

Add '-4.875' to each side of the equation.
4.875 + -4.25x + -4.875 + x2 = 0 + -4.875

Reorder the terms:
4.875 + -4.875 + -4.25x + x2 = 0 + -4.875

Combine like terms: 4.875 + -4.875 = 0.000
0.000 + -4.25x + x2 = 0 + -4.875
-4.25x + x2 = 0 + -4.875

Combine like terms: 0 + -4.875 = -4.875
-4.25x + x2 = -4.875

The x term is -4.25x.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x + 4.515625 + x2 = -4.875 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = -4.875 + 4.515625

Combine like terms: -4.875 + 4.515625 = -0.359375
4.515625 + -4.25x + x2 = -0.359375

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = -0.359375

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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