Final answer:
The solutions to the quadratic equation z² + 14z + 48 = 0 are found by factoring the equation into (z + 6)(z + 8) = 0 and solving for z, which gives z = -6 and z = -8.
Step-by-step explanation:
To solve the quadratic equation z² + 14z + 48 = 0, we can either factor the equation or use the quadratic formula. Since the equation factors easily, we can rewrite it as (z + 6)(z + 8) = 0. Setting each factor equal to zero, we find the two solutions for z:
- z + 6 = 0 → z = -6
- z + 8 = 0 → z = -8
Therefore, the solutions to the quadratic equation are z = -6 and z = -8.