#### Answer

The solution is $x=5$

#### Work Step by Step

$(x-9)(x-1)=-16$
Evaluate the product on the left side:
$x^{2}-x-9x+9=-16$
Take $16$ to the left side and simplify:
$x^{2}-x-9x+9+16=0$
$x^{2}-10x+25=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. In this case, $a=1$, $b=-10$ and $c=25$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-10)\pm\sqrt{(-10)^{2}-4(1)(25)}}{2(1)}=\dfrac{10\pm\sqrt{100-100}}{2}=...$
$...=\dfrac{10\pm\sqrt{0}}{2}=\dfrac{10}{2}=5$
The solution is $x=5$