Step 1 :The given equation is \(x^{2}+4 x+4=0\).
Step 2 :We can solve this equation using the quadratic formula, which is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Step 3 :In this equation, \(a = 1\), \(b = 4\), and \(c = 4\).
Step 4 :Substitute these values into the quadratic formula to find the solutions for \(x\).
Step 5 :The discriminant \(D = b^2 - 4ac = 0\).
Step 6 :Since the discriminant is 0, the equation has one unique solution.
Step 7 :The solution is \(x = -2\).
Step 8 :Final Answer: \(\boxed{-2}\)