Question

Solve the following equation using the quadratic formula.

Answer 1

Answer:

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

Step-by-step explanation:

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

Use the quadratic formula.

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

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

$\frac{-\left(-8\right)\pm\sqrt{\left(-8\right)^2-4\times 1\times 97}}{2\times 1}$

Evaluate.

$\frac{8\pm\sqrt{324}i}{2\times 1}$

$\frac{8\pm18i}{2}$

$4\pm9i$

Answer 2

Answer:

x = 4   ±9i

Step-by-step 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