Respuesta :

apologiabiology
use quadratic formula

for ax^2+bx+c=0

x=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]

1x^2+2x+9=0
a=1
b=2
c=9
remember
i=√-1 or
i²=-1


x=[tex] \frac{-2+/- \sqrt{2^2-4(1)(9)} }{2(1)} [/tex]
x=[tex] \frac{-2+/- \sqrt{4-36} }{2} [/tex]
x=[tex] \frac{-2+/- \sqrt{-32} }{2} [/tex]
x=[tex] \frac{-2+/- 4\sqrt{-2} }{2} [/tex]
x=[tex] \frac{-2+/- 4\sqrt{-2} }{2} [/tex]
x=[tex] \frac{-2+/- 4i\sqrt{2} }{2} [/tex]
x=[tex] -1+ 2i\sqrt{2}  [/tex] or [tex] -1- 2i\sqrt{2}  [/tex]


SociometricStar

Answer:

[tex]x=-1+2\sqrt{2}i,\:x=-1-2\sqrt{2}i[/tex]

Step-by-step explanation:

We have been given the quadratic equation [tex]x^2+2x+9=0[/tex]

The quadratic formula is given by

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Comparing the given equation with [tex]ax^2+bx+c=0[/tex]

[tex]a=1,\:b=2,\:c=9[/tex]

Substituting the known values, we get

[tex]x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \:9}}{2\cdot \:1}\\\\\frac{-2\pm\sqrt{32}i}{2\cdot \:1}\\\\\frac{-2\pm4\sqrt{2}i}{2}\\\\-1\pm2\sqrt{2}i[/tex]

Hence, the values of x are

[tex]x=-1+2\sqrt{2}i,\:x=-1-2\sqrt{2}i[/tex]

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