Let's simplify the expression step by step:
The expression is:
[
\frac{1}{8} \times \left(-\frac{1}{8} - 8\right) + \left(-\frac{1}{8} - 6\right) \times \left(-\frac{1}{8} - 6\right)
]
First, calculate (-\frac{1}{8} - 8):
[
-\frac{1}{8} - 8 = -\frac{1}{8} - \frac{64}{8} = -\frac{1 + 64}{8} = -\frac{65}{8}
]
Now, substitute this back into the expression:
[
\frac{1}{8} \times \left(-\frac{65}{8}\right) + \left(-\frac{1}{8} - 6\right) \times \left(-\frac{1}{8} - 6\right)
]
Now calculate (\frac{1}{8} \times -\frac{65}{8}):
[
\frac{1}{8} \times -\frac{65}{8} = -\frac{65}{64}
]
Next, calculate (-\frac{1}{8} - 6):
[
-\frac{1}{8} - 6 = -\frac{1}{8} - \frac{48}{8} = -\frac{49}{8}
]
Now we need to compute (\left(-\frac{49}{8}\right) \times \left(-\frac{49}{8}\right)):
[
\left(-\frac{49}{8}\right)^2 = \frac{49^2}{8^2} = \frac{2401}{64}
]
Now we can put it all back into the original expression:
[
-\frac{65}{64} + \frac{2401}{64}
]
This is equivalent to:
[
\frac{-65 + 2401}{64} = \frac{2336}{64}
]
Finally, simplify (\frac{2336}{64}):
[
2336 \div 64 = 36.5
]
Thus, the final answer is:
[
\boxed{36.5}
]
