Determine the positive values of `' k '` for which the equation `x^2+k x+64=0` and `x^2-8x+k=0` will both have real roots.

Explanation

To determine the positive values of \( k \) for which the equations \( x^2 + kx + 64 = 0 \) and \( x^2 - 8x + k = 0 \) both have real roots, we need to analyze the discriminants of both equations.

### Step 1: Analyze the first equation
The first equation is:
\[ x^2 + kx + 64 = 0 \]
The discriminant \( D_1 \) of this quadratic equation is given by:
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