(16x^2)-128x+314=0

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Solution for (16x^2)-128x+314=0 equation: 


Simplifying
(16x2) + -128x + 314 = 0

Reorder the terms:
314 + -128x + (16x2) = 0

Solving
314 + -128x + (16x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(157 + -64x + (8x2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(157 + -64x + (8x2))' equal to zero and attempt to solve:

Simplifying
157 + -64x + (8x2) = 0

Solving
157 + -64x + (8x2) = 0

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

Divide each side by '8'.
19.625 + -8x + x2 = 0

Move the constant term to the right:

Add '-19.625' to each side of the equation.
19.625 + -8x + -19.625 + x2 = 0 + -19.625

Reorder the terms:
19.625 + -19.625 + -8x + x2 = 0 + -19.625

Combine like terms: 19.625 + -19.625 = 0.000
0.000 + -8x + x2 = 0 + -19.625
-8x + x2 = 0 + -19.625

Combine like terms: 0 + -19.625 = -19.625
-8x + x2 = -19.625

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -19.625 + 16

Reorder the terms:
16 + -8x + x2 = -19.625 + 16

Combine like terms: -19.625 + 16 = -3.625
16 + -8x + x2 = -3.625

Factor a perfect square on the left side:
((x) + -4)((x) + -4) = -3.625

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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