Answer
$x=\left\{ 3,5 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the solutions of the given equation, $
x^2-8x+15=0
,$ use the Quadratic Formula.
$\bf{\text{Solution Details:}}$
Using the form $ax^2+bx+c=0,$ the quadratic equation above has $a=
1
, b=
-8
, c=
15
.$ Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, then
\begin{array}{l}\require{cancel}
x=\dfrac{-(-8)\pm\sqrt{(-8)^2-4(1)(15)}}{2(1)}
\\\\
x=\dfrac{8\pm\sqrt{64-60}}{2}
\\\\
x=\dfrac{8\pm\sqrt{4}}{2}
\\\\
x=\dfrac{8\pm2}{2}
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
x=\dfrac{8-2}{2}
\\\\
x=\dfrac{6}{2}
\\\\
x=3
\\\\\text{OR}\\\\
x=\dfrac{8+2}{2}
\\\\
x=\dfrac{10}{2}
\\\\
x=5
.\end{array}
Hence, $
x=\left\{ 3,5 \right\}
.$
