Answer
$x=1
\text{ and }
x=4$
Work Step by Step
Using the properties of equality, the given equation, $
x(x-5)=-4
,$ is equivalent to
\begin{align*}
x(x)+x(-5)&=-4
&\text{ (use Distributive Property)}
\\
x^2-5x&=-4
\\
x^2-5x+4&=0
\end{align*}
In the equation above, $a=
1
,$ $b=
-5
,$ and $c=
4
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(4)}}{2(1)}
\\\\&=
\dfrac{5\pm\sqrt{25-16}}{2}
\\\\&=
\dfrac{5\pm\sqrt{9}}{2}
\\\\&=
\dfrac{5\pm3}{2}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{5-3}{2} &\text{ OR }& \dfrac{5+3}{2}
\\\\&
=\dfrac{2}{2} &\text{ OR }& =\dfrac{8}{2}
\\\\&
=1 &\text{ OR }& =4
\end{array}
Hence, the solutions are $
x=1
\text{ and }
x=4
.$
