Answer:
[tex]x= 2.8[/tex]
or
[tex]x=-4.3[/tex]
I chose the quadratic formula because I could not factor the quadratic.
Step-by-step explanation:
First of all let's work out what [tex]k(2)[/tex] equals to. We can do this by replacing every [tex]x[/tex] term in [tex]k(x)[/tex] with a 2.
So: [tex]k(2) = 2(2) + 12 = 4 + 12 = 16[/tex]
Now let's set up our equation [tex]g(x) = 2 * k(2)[/tex]. Replace the functions with what we know they equal to.
[tex]2x^2+3x+8=2*16=32[/tex]
Now bring all the terms to one side:
[tex]2x^2+3x-24=0[/tex]
Now we can solve this quadratic for [tex]x[/tex].
I'll put this into the quadratic formula because it cannot be factored.
[tex]x=\frac{-b\frac{+}{-} \sqrt{b^2-4ac} }{2a}[/tex], Compare our quadratic to the general equation of a quadratic: [tex]ax^2+bx+c=0[/tex].
[tex]a=2,b=3, c=-24[/tex]
Now put these terms into the quadratic formula to get the values for [tex]x[/tex].
[tex]x=\frac{-3\frac{+}{-} \sqrt{(3)^2-4(2)(-24)} }{2(2)}[/tex]
So: [tex]x=\frac{-3+\sqrt{201} }{4}[/tex]=2.8 (1 decimal place)
or
[tex]x=\frac{-3-\sqrt{201} }{4}[/tex]= -4.3 (1 decimal place)
