Question

Need to know this now pls !!! NEED THE PROCESS , TOO!!! x squared - 18x = -117

Answer 1

Answer:

$x_1=9+6i$

$x_2=9-6i$

Step-by-step explanation:

Given:

$x^2-18x=-117$

Rewrite as a quadratic equation:

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

Use the quadratic formula:

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

$x=\frac{-(-18)\pm\sqrt{(-18)^2-4(1)(117)}}{2(1)}$

$x=\frac{18\pm\sqrt{324-468}}{2}$

$x=\frac{18\pm\sqrt{-144}}{2}$ <-- No real solutions since discriminant is negative

Continuation:

$x=\frac{18\pm\sqrt{-1*144}}{2}$

$x=\frac{18\pm\sqrt{-1}\sqrt{144}}{2}$

$x=\frac{18\pm12i}{2}$ <-- Recall that $\sqrt{-1}=i$

$x=9\pm6i$

Solutions:

$x_1=9+6i$

$x_2=9-6i$

Answer 2

Answer:

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

Step-by-step 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