Question

Solve for x in the equation x² -8x + 41 = 0

Answer 1

x=4+5i and x=4-5i

Explanation:

`x^2-8x + 41 = 0`

we apply quadratic formula to solve for x

`x=(-b+-√(b^2-4ac))/(2a)`

a= 1, b= -8 and c= 41

Plug in all the values in the formula

`x=(-b+-√(b^2-4ac))/(2a)`

`x=(-(-8)+-√((-8)^2-4(1)(41)))/(2(1))`

`x=(8+-√(64-164))/(2)`

`x=(8+-√(-100))/(2)`

square root (-1) is 'i'

`x=(8+-10i)/(2)`

Divide both terms by 2

x= 4+-5i

two values of x are 4+5i and 4-5i