Solving Quadratic Inequalities By Completing the Square

We can solve any quadratic inequality by completing the square.
Example: Solve

\[x^2-6x-16 \lt 0\]

Completing the square gives

\[(x-3)^2 -(-3)^2-16 = (x-3)^2-25 \lt 0\]

Hence

\[(x-3)^2 \lt 25\]

.
Taking the square root gives

\[-5 \lt x-3 \lt 5\]

.
Now add 3 to give

\[-2 \lt x \lt 8\]