Final answer:
To factor the quadratic 5z²+9z-14, we find two numbers whose product is -70 and whose sum is 9. The factored form is (z + 14)(5z - 1) = 0, and the solutions are z = -14 and z = 1/5.
Step-by-step explanation:
This expression is a quadratic equation of the form 5z²+9z-14 = 0, where the constants are a = 5, b = 9, and c = -14. To factor this quadratic, we need to find two numbers whose product is ac (5 * -14 = -70) and whose sum is b (9). After trying different combinations, we find that the numbers are 14 and -5.
So, we can rewrite the quadratic as (z + 14)(5z - 1) = 0. Therefore, the solutions to the equation are z = -14 and z = 1/5.