$x=\pm10$  

 $x=\sqrt{10}$  

 $x=\pm\sqrt{10}$  

No real solutions

 $x=-20$  

 $x=\pm2\sqrt{5}$  

 $x=-2\sqrt{5}$  

No real solutions

 $x=\pm6$  

 $x=\pm36$  

 $x=\pm18$  

No real solutions

 $x=6\ or\ x=4$  

 $x=\pm\sqrt{14}$  

 $x=-6\ or\ x=-4$  

No real solutions

 $x=3\ or\ x=-5$  

 $x=\pm\sqrt{13}$  

 $x=-3\ or\ x=5$  

No real solutions

 $x=-2\ or\ x=-8$  

 $x=\pm\sqrt{6}$  

 $x=2\ or\ x=8$  

No real solutions

 $x=1\ or\ x=9$  

 $x=-1\ or\ x=-9$  

 $x=-2\ or\ x=-18$  

No real solutions

 $x=2\ or\ x=-8$  

 $x=-1\ or\ x=4$  

 $x=1\ or\ x=-4$  

No real solutions

 $x=2\ or\ x=5$  

 $x=-2\ or\ x=-5$  

 $x=4\ or\ x=10$  

No real solutions

 $x=\frac{3\pm\sqrt{29}}{5}$  

 $x=\frac{8}{5}\ or\ x=-\frac{2}{5}$  

 $x=\frac{-3\pm\sqrt{29}}{10}$  

No real solutions

When you cannot factor it

When it begins with a negative leading coefficient

When there is a square root of a negative number

When it only has two terms

When its highest exponent (degree) is 1

When its highest exponent (degree) is 2

When its highest exponent (degree) is 3

When you cannot factor the quadratic