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

### Step 2: Simplify the equation
Calculating \( (-4)^2 \):
\[ 16 + k(-4) + 8 = 0 \]
This simplifies to:
\[ 16 - 4k + 8 = 0 \]

### Step 3: Combine like terms
Now, combine \( 16 \) and \( 8 \):
\[ 24 - 4k = 0 \]

### Step 4: Isolate the term with \( k \)
To isolate the term with \( k \), we can move \( 4k \) to the right side:
\[ 24 = 4k \]

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

### Conclusion
Thus, the value of \( k \) is \( 6 \).

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