Final answer:
To solve the equation 3z² + 6z + 3 = 0, we can use the quadratic formula. The equation has one solution, which is z = -1.
Step-by-step explanation:
To solve the equation 3z² + 6z + 3 = 0, we can use the quadratic formula. For an equation of the form ax² + bx + c = 0, the quadratic formula is:
z = (-b ± √(b² - 4ac)) / (2a)
Using the values from the given equation, a = 3, b = 6, and c = 3, we can substitute them into the formula and calculate the solutions for z.
z = (-6 ± √(6² - 4 * 3 * 3)) / (2 * 3)
z = (-6 ± √(36 - 36)) / 6
z = (-6 ± √0) / 6
Since the discriminant (√(b² - 4ac)) is 0, the equation has only one solution.
z = -6 / 6
z = -1