Answer:
x=4+5i and x=4-5i
Step-by-step explanation:
[tex]x^2-8x + 41 = 0[/tex]
we apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a= 1, b= -8 and c= 41
Plug in all the values in the formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-8)+-\sqrt{(-8)^2-4(1)(41)}}{2(1)}[/tex]
[tex]x=\frac{8+-\sqrt{64-164}}{2}[/tex]
[tex]x=\frac{8+-\sqrt{-100}}{2}[/tex]
square root (-1) is 'i'
[tex]x=\frac{8+-10i}{2}[/tex]
Divide both terms by 2
x= 4+-5i
two values of x are 4+5i and 4-5i
