Solving Quadratic Equations & Complex Numbers

Solve the following quadratic equation:
 $-3m^2=108$  

•  $x=2i\sqrt{6}\ \&\ x=-2i\sqrt{6}$  

•  $x=6i$  

•  $x=6i\ \&\ x=-6i$  

•  $x=36\ \&\ x=-36$  

Solve the following quadratic equation:
 $n^2+7=-13$  

•  $x=6\ \&\ x=-6$  

•  $x=2i\sqrt{5}\ \&\ x=-2i\sqrt{5}$  

•  $x=2i\sqrt{5}$  

•  $x=2\sqrt{23}\ \&\ x=-2\sqrt{23}$  

Solve the following quadratic equation:
 $9x^2+9==-89$  

•  $x=3i\ \&\ x=-3i$  

•  $x=\frac{i\sqrt{22}}{2}\ \&\ x=-\frac{i\sqrt{22}}{2}$  

•  $x=\frac{7i\sqrt{2}}{3}\ \&\ x=-\frac{7i\sqrt{2}}{3}$  

•  $x=\frac{4i\sqrt{5}}{3}$  

Solve the following quadratic equation:
 $7m^2-10=-64$  

•  $x=\frac{3i\sqrt{42}}{7}\ \&\ x=-\frac{3i\sqrt{42}}{7}$  

•  $x=\frac{i\sqrt{518}}{7}\ \&\ x=-\frac{i\sqrt{518}}{7}$  

•  $x=\frac{i\sqrt{141}}{3}\ \&\ x=-\frac{i\sqrt{141}}{3}$  

•  $x=i\sqrt{6}\ \&\ x=-i\sqrt{6}$  

Solve the following quadratic equation by completing the square:
 $p^2-4p-3=-9$  

•  $x=9+3\sqrt{14}\ \&\ x=9-3\sqrt{14}$  

•  $x=15\ \&\ x=3$  

•  $x=2+i\sqrt{2}\ \&\ x=2-i\sqrt{2}$  

•  $x=18+3i\sqrt{31}\ \&\ x=18-3i\sqrt{31}$  

Solve the following quadratic equation by completing the square:
 $x^2+14x+55=-2$  

•  $x=-7+2i\sqrt{2}\ \&\ x=-7-2i\sqrt{2}$  

•  $x=15\ \&\ x=-3$  

•  $x=7+i\sqrt{22}\ \&\ x=7-i\sqrt{22}$  

•  $x=-7+i\sqrt{106}\ \&\ x=-7-i\sqrt{106}$  

Solve the following quadratic equation by completing the square:
 $2x^2-16x+59=-4$  

•  $x=\frac{-3+2i\sqrt{3}}{3}\ \&\ x=\frac{-3-2i\sqrt{3}}{3}$  

•  $x=\frac{8+i\sqrt{62}}{2}\ \&\ x=\frac{8-i\sqrt{62}}{2}$  

•  $x=-2+i\sqrt{15}\ \&\ x=-2-i\sqrt{15}$  

•  $x=2+i\sqrt{7}\ \&\ x=2-i\sqrt{7}$  

Solve the following quadratic equation by completing the square:
 $9x^2+18x+65=-8$  

•  $x=\frac{3}{2}\ \&\ x=-\frac{7}{2}$  

•  $x=\frac{-3+8i}{3}\ \&\ x=\frac{-3-8i}{3}$  

•  $x=-8+i\sqrt{106}\ \&\ x=-8-i\sqrt{106}$  

•  $x=2+i\sqrt{21}\ \&\ x=2-i\sqrt{21}$  

Solve the following quadratic equation by using the quadratic formula:
 $12x^2+3x+12=0$  

•  $x=\frac{\sqrt{15}}{2}\ \&\ x=-\frac{\sqrt{15}}{2}$  

•  $x=\frac{-1+i\sqrt{15}}{8}\ \&\ x=\frac{-1-i\sqrt{15}}{8}$  

•  $x=\frac{1+3i\sqrt{7}}{8}\ \&\ x=\frac{1-3i\sqrt{7}}{8}$  

•  $x=\frac{-1+3i\sqrt{7}}{8}\ \&\ x=\frac{-1-3i\sqrt{7}}{8}$  

Solve the following quadratic equation by using the quadratic formula:
 $5x^2-7x+11=0$  

•  $x=\frac{-1+i\sqrt{7}}{2}\ \&\ x=\frac{-1-i\sqrt{7}}{2}$  

•  $x=\frac{1+i\sqrt{23}}{2}\ \&\ x=\frac{1-i\sqrt{23}}{2}$  

•  $x=2\ \&\ x=-3$  

•  $x=\frac{7+3i\sqrt{19}}{10}\ \&\ x=\frac{7-3i\sqrt{19}}{10}$