1. The problem states that $x=3$ is a solution to the quadratic equation $$x^2 + kx + 15 = 0.$$ We need to find the value of $k$. 2. Since $x=3$ is a root, it must satisfy the equation. Substitute $x=3$ into the equation: $$3^2 + k(3) + 15 = 0.$$ 3. Simplify the expression: $$9 + 3k + 15 = 0.$$ 4. Combine like terms: $$24 + 3k = 0.$$ 5. Solve for $k$: $$3k = -24$$ $$k = \frac{-24}{3} = -8.$$ 6. Therefore, the value of $k$ is $-8$. This means the quadratic equation with $k=-8$ has $x=3$ as a root.