## 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
$-5 \lt x-3 \lt 5$
.
$-2 \lt x \lt 8$