Answer
$x=5$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(x-9)(x-1)=-16
,$ use the FOIL Method and express the equation in the form $ax^2+bx+c=0.$ Then use the Quadratic Formula.
$\bf{\text{Solution Details:}}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel}
x(x)+x(-1)-9(x)-9(-1)=-16
\\\\
x^2-x-9x+9=-16
\\\\
x^2+(-x-9x)+(9+16)=0
\\\\
x^2-10x+25=0
.\end{array}
In the equation above, $a=
1
,$ $b=
-10,$ and $c=
25
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{array}{l}\require{cancel}
x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4(1)(25)}}{2(1)}
\\\\
x=\dfrac{10\pm\sqrt{100-100}}{2}
\\\\
x=\dfrac{10\pm\sqrt{0}}{2}
\\\\
x=\dfrac{10}{2}
\\\\
x=5
.\end{array}
The solution is $
x=5
.$
