Step 1: Let the two consecutive negative integers be $x$ and $x + 1$.
Step 2: According to the question :
$$x^2 + (x+1)^2 = 481$$
Step 3: Expand and simplify.
$$x^2 + x^2 + 2x + 1 = 481 \Rightarrow 2x^2 + 2x - 480 = 0$$
$$\Rightarrow x^2 + x - 240 = 0$$
Step 4: Factorise by splitting the middle term ($16 \times 15 = 240$, $16 - 15 = 1$) :
$$x^2 + 16x - 15x - 240 = 0$$
$$x(x + 16) - 15(x + 16) = 0 \Rightarrow (x + 16)(x - 15) = 0$$
Step 5: $$x = -16 \quad \text{or} \quad x = 15$$
Step 6: Since the integers are NEGATIVE, we reject $x = 15$ and take $x = -16$.
Hence the required integers are $-16$ and $-15$.
Check : $(-16)^2 + (-15)^2 = 256 + 225 = 481$ \checkmark