Question

Solve for x using completing the square: V^2-6v=-91

Answer 1

$(*)\qquad(a-b)^2=a^2-2ab+b^2\\\\v^2-6v=-91\\\\v^2-2\cdot v\cdot3=-91\ \ \ \ |+3^2\\\\\underbrace{v^2-2\cdot v\cdot3+3^2}_{(*)}=-91+3^2\\\\(v-3)^2=-82 < 0-NO\ REAL\ SOLUTION\\\\COMPLEX\ SOLUTIONS\\\\v-3=\pm\sqrt{-82}\\\\v-3=-i\sqrt{82}\ \vee\ v-3=i\sqrt{82}\ \ \ \ \ |+3\\\\\boxed{x=3-i\sqrt{82}\ \vee\ v=3+i\sqrt{82}}$