Answer:
The solutions to the equation are:
[tex]\begin{gathered} x=-3.24 \\ or \\ x=5.24 \end{gathered}[/tex]Explanation:
Given the equation below;
[tex]x^2-2x-17=0[/tex]We want to find the solutions of the quadratic equation.
Applying the quadratic formula;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}_{}}{2a}[/tex]from the given equation;
[tex]\begin{gathered} a=1 \\ b=-2 \\ c=-17 \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(1)(-17)}}{2(1)} \\ x=\frac{2\pm\sqrt[]{4^{}+68}}{2} \\ x=\frac{2\pm\sqrt[]{72}}{2} \\ x=\frac{2\pm2\sqrt[]{18}}{2} \\ x=1\pm\sqrt[]{18} \\ \\ x=1-\sqrt[]{18} \\ x=-3.24 \\ or \\ x=1+\sqrt[]{18} \\ x=5.24 \end{gathered}[/tex]Therefore, the solutions to the equation are;
[tex]\begin{gathered} x=-3.24 \\ or \\ x=5.24 \end{gathered}[/tex]