Respuesta :

Answer:

[tex]x_1=-4+2i\\x_2=-4-2i[/tex]

Step-by-step explanation:

A quadratic function ([tex]ax^2+bx+c=0[/tex]) usually has two solutions for x. To find that solutions we have to use Bhaskara's Formula:

[tex]x_1=\frac{-b+\sqrt{b^2-4ac}}{2a}\\and\\x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

We have the expression:

[tex]x^2+8x+20=0[/tex]

Where,

[tex]a=1, b=8,c=20[/tex]

Then, applying Bhaskara's Formula:

[tex]x_1=\frac{-8+\sqrt{8^2-4.1.20}}{2.1}=\frac{-8+\sqrt{64-80}}{2}\\\\x_1=\frac{-8+\sqrt{-16}}{2}=\frac{-8+\sqrt{-1}\sqrt{16}}{2}\\\\x_1=\frac{-8+i4}{2}\\\\x_1=-4+2i[/tex]

Remember that: [tex]\sqrt{-1}=i[/tex]

We have the first solution for x, now we have to find the second:

[tex]x_2=\frac{-8-\sqrt{8^2-4.1.20}}{2.1}=\frac{-8-\sqrt{64-80}}{2}\\\\x_2=\frac{-8-\sqrt{-16}}{2}=\frac{-8-\sqrt{-1}\sqrt{16}}{2}\\\\x_2=\frac{-8-i4}{2}\\\\x_2=-4-2i[/tex]

Then the solutions for x are:

[tex]x_1=-4+2i\\x_2=-4-2i[/tex]

Over the complex numbers.

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