Answer:
The answer is
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]
Step-by-step explanation:
x² + 10x + 89 = 0
Using the quadratic formula
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
From the question
a = 1 , b = 10 , c = 89
Substitute the values into the above formula and solve
We have
[tex]x = \frac{ - 10\pm \sqrt{ {10}^{2} - 4(1)(89)} }{2(1)} \\ = \frac{ - 10\pm \sqrt{100 - 356} }{2} \\ = \frac{ - 10\pm \sqrt{ - 256} }{2} \\ = \frac{10\pm 16 \: i}{2} [/tex]
Separate the real and imaginary part
That's
[tex]x = - \frac{10}{2} \pm \frac{16}{2} \: i \\ x = - 5\pm8 \: i[/tex]
We have the final answer as
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]
Hope this helps you
