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
\[-2 \lt x \lt 8\]
. Solving Quadratic Inequalities By Completing the Square
We can solve any quadratic inequality by completing the square.
Example: Solve
Completing the square gives
Hence
Taking the square root gives
Now add 3 to give
Example: Solve
Completing the square gives
Hence
Taking the square root gives
Now add 3 to give