To find the possible values of z in the quadratic equation z² + 4z + 4 = 0, we can first try factoring the equation.
The expression z² + 4z + 4 can be factored as:
(z + 2)(z + 2) = 0
Thus, we can rewrite the equation as:
(z + 2)² = 0
Next, to find the values of z, we can set the factor equal to zero:
z + 2 = 0
Solving for z, we subtract 2 from both sides:
z = -2
Since the factored form was a perfect square, -2 is a repeated root of the equation. Thus, the only possible value of z is:
z = -2
In conclusion, the quadratic equation z² + 4z + 4 = 0 has a single possible value for z, which is -2.