Answer:
Option 1) [tex]x=-2+i\sqrt{2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +4x+6=0[/tex]
so
[tex]a=1\\b=4\\c=6[/tex]
substitute in the formula
[tex]x=\frac{-4\pm\sqrt{4^{2}-4(1)(6)}} {2(1)}[/tex]
[tex]x=\frac{-4\pm\sqrt{-8}} {2}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{-4\pm i\sqrt{8}} {2}[/tex]
[tex]x=\frac{-4\pm2i\sqrt{2}} {2}[/tex]
[tex]x=-2\pm i\sqrt{2}[/tex]
The solutions are
[tex]x=-2+i\sqrt{2}[/tex]
and
[tex]x=-2-i\sqrt{2}[/tex]
