Respuesta :

Answer:

Answer: approximately -1.63 and -7.37

Step-by-step explanation:

First of all, let's expand the parenthesis by multiplying x into both of its terms.

[tex]x(x+9)+12 = 0\\x^2+9x+12=0[/tex]

We get the equation:

[tex]x^2+9x+12=0[/tex]

The quadratic formula looks like this

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

where the equation is of the form

[tex]ax^{2}+bx+c=0[/tex]

Comparing this to our equation above,

[tex]x^2+9x+12=0[/tex]

we can see that

[tex]a = 1\\b= 9\\c= 12[/tex]

Let's put these values into the quadratic formula.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-9\pm\sqrt{9^2-4*1*12}}{2*1}\\x=\frac{-9\pm\sqrt{9^2-48}}{2}\\x=\frac{-9\pm\sqrt{81-48}}{2}\\x=\frac{-9\pm\sqrt{33}}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x_{1}=\frac{-9+5.744...}{2}=\frac{-3.255...}{2}=-1.62771867\\x_{2}=\frac{-9-5.744...}{2}=\frac{-14.744...}{2}=-7.3722813\\[/tex]

Answer: approximately -1.63 and -7.37

You can also choose not to approximate the square root of 33, and you'd receive the answers:

[tex]x_{1}=\frac{-9+\sqrt{33}}{2}\\x_{2}=\frac{-9-\sqrt{33}}{2}[/tex]

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