Question

Solve the following equation using the quadratic formula.

x^2 - 8x + 97 = 0
А.x = 8 + 18i and x = 8 – 18i
B.x= 8 + 18i and x = 8 - 18i
C.x= 4 + 9i and x = 4 - 9i
D. x= 4 + 9i and x= -4 - 9i

Answer 1

C. x= 4 + 9i or x = 4 - 9i

Explanation:

`x^2 - 8x + 97 = 0`

Use the quadratic formula.

`(-b\pm √(b^2-4ac))/(2a)`

Substitute a = 1, b = -8, and c = 97.

`(-\left(-8\right)\pm√(\left(-8\right)^2-4* 1* 97))/(2* 1)`

Evaluate.

`(8\pm√(324)i)/(2* 1)`

`(8\pm18i)/(2)`

`4\pm9i`

Answer 2

x = 4 ±9i

Explanation:

x^2 - 8x + 97 = 0

Complete the square by subtracting 97 from each side

x^2 - 8x =- 97

Take the coefficient of x

-8 and divide by 2

-8/2 = -4

Then square it

(-4)^2 = 16

Add it to each side

x^2 - 8x + 16 = -97+16

(x-4)^2 = -81

Take the square root of each side

x-4 = ±sqrt(-81)

x-4 = ±9i

Add 4 to each side

x = 4 ±9i