Answer:
[tex]x_1=9+6i[/tex]
[tex]x_2=9-6i[/tex]
Step-by-step explanation:
Given:
[tex]x^2-18x=-117[/tex]
Rewrite as a quadratic equation:
[tex]x^2-18x+117=0[/tex]
Use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-18)\pm\sqrt{(-18)^2-4(1)(117)}}{2(1)}[/tex]
[tex]x=\frac{18\pm\sqrt{324-468}}{2}[/tex]
[tex]x=\frac{18\pm\sqrt{-144}}{2}[/tex] <-- No real solutions since discriminant is negative
Continuation:
[tex]x=\frac{18\pm\sqrt{-1*144}}{2}[/tex]
[tex]x=\frac{18\pm\sqrt{-1}\sqrt{144}}{2}[/tex]
[tex]x=\frac{18\pm12i}{2}[/tex] <-- Recall that [tex]\sqrt{-1}=i[/tex]
[tex]x=9\pm6i[/tex]
Solutions:
[tex]x_1=9+6i[/tex]
[tex]x_2=9-6i[/tex]
