Answer:
A. {[tex]3+7i,3-7i[/tex]}
Step-by-step explanation:
The given equation is [tex]x^2-6x+58=0[/tex]
Use the quadratic formula with a=1,b=-6 and c=58
Recall the quadratic formula;
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
We substitute the given values to get;
[tex]x=\frac{--6\pm \sqrt{(-6)^2-4(1)(58)} }{2(1)}[/tex]
[tex]x=\frac{6\pm \sqrt{36-232} }{2}[/tex]
[tex]x=\frac{6\pm \sqrt{-196} }{2}[/tex]
Recall that;
[tex]\sqrt{-1}=i[/tex]
[tex]x=\frac{6\pm 14i}{2}[/tex]
[tex]x=3\pm 7i[/tex]
[tex]x=3+7i[/tex] or [tex]x=3-7i[/tex]
