Answer:
[tex]x=4-9i[/tex] or [tex]x=4+9i[/tex]
Step-by-step explanation:
The given equation is
[tex]x^2-8x+97=0[/tex]
By comparing to [tex]ax^2+bx+c=0[/tex], we have a=1,b=-8 and c= 97.
The quadratic formula is;
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
We substitute the values to obtain;
[tex]x=\frac{--8\pm\sqrt{(-8)^2-4(1)(97)} }{2(1)}[/tex]
[tex]x=\frac{8\pm\sqrt{-324} }{2}[/tex]
[tex]x=\frac{8\pm18i }{2}[/tex]
[tex]x=4\pm9i[/tex]
Therefore [tex]x=4-9i[/tex] or [tex]x=4+9i[/tex]
