If `-4` is a solution for x in the equation `x^2 + kx + 8 = 0`, what is k?

Answer

To find the value of \( k \) in the equation \( x^2 + kx + 8 = 0 \) given that \( -4 \) is a solution, we can follow these steps:

### Step 1: Substitute the value of \( x \)
Since \( -4 \) is a solution, we substitute \( x = -4 \) into the equation:
\[ (-4)^2 + k(-4) + 8 = 0 \]

### Step 2: Calculate \( (-4)^2 \)
Calculating \( (-4)^2 \):
\[ 16 + k(-4) + 8 = 0 \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ 16 - 4k + 8 = 0 \]
Combine \( 16 \) and \( 8 \):
\[ 24 - 4k = 0 \]

### Step 4: Isolate \( k \)
Now, isolate \( k \) by moving \( 4k \) to the other side:
\[ 24 = 4k \]

### Step 5: Solve for \( k \)
Now, divide both sides by \( 4 \):
\[ k = \frac{24}{4} = 6 \]

### Final Answer
Thus, the value of \( k \) is:
\[ \boxed{6} \]