Answer:
[tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]
Step-by-step explanation:
Roots of quadratic equations [tex]ax^{2}+bx+c=0[/tex] calculated as:
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
First, compare [tex]ax^{2}+bx+c=0[/tex] with [tex]x^{2}+2x-22=0[/tex]
here a = 1 , b = 2 and c = -22
Now, plug the value of a,b and c in [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x=\frac{-2\pm \sqrt{2^{2}-4(1)(-22)}}{2(1)}[/tex]
[tex]x=\frac{-2\pm \sqrt{4+88}}{2}[/tex]
[tex]x=\frac{-2\pm \sqrt{92}}{2}[/tex]
[tex]x=\frac{-2\pm 2\sqrt{23}}{2}[/tex]
[tex]x=-1\pm \sqrt{23}[/tex]
Hence, [tex]x=-1+\sqrt{23}\; ,\;-1-\sqrt{23}[/tex]