Question

Need to know this now pls !!! NEED THE PROCESS , TOO!!!

x squared - 18x = -117

Answer 1

`x_1=9+6i`

`x_2=9-6i`

Explanation:

Given:

`x^2-18x=-117`

Rewrite as a quadratic equation:

`x^2-18x+117=0`

Use the quadratic formula:

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-(-18)\pm√((-18)^2-4(1)(117)))/(2(1))`

`x=(18\pm√(324-468))/(2)`

`x=(18\pm√(-144))/(2)` <-- No real solutions since discriminant is negative

Continuation:

`x=(18\pm√(-1*144))/(2)`

`x=(18\pm√(-1)√(144))/(2)`

`x=(18\pm12i)/(2)` <-- Recall that
`√(-1)=i`

`x=9\pm6i`

Solutions:

`x_1=9+6i`

`x_2=9-6i`

Answer 2

x = 9 + 6i or x = 9 - 6i

Explanation:

x² - 18x + 117 = 0

Complete the square and solve:

(x - 9)² - 81 + 117 = 0

(x - 9)² + 36 = 0

(x - 9)² = -36

x - 9 = ±sqrt(-36)

x - 9 = ±sqrt(-1).sqrt(36)

i = imaginary number = sqrt(-1)

x - 9 = ±6i

x = 9 ± 6i

There are no real solutions, only imaginary ones

9 + 6i and 9 - 6i