Question

PLEASE HELP

Answer 1

Answer:

$x= 2.8$

or

$x=-4.3$

I chose the quadratic formula because I could not factor the quadratic.

Step-by-step explanation:

First of all let's work out what $k(2)$ equals to. We can do this by replacing every $x$ term in $k(x)$ with a 2.

So: $k(2) = 2(2) + 12 = 4 + 12 = 16$

Now let's set up our equation $g(x) = 2 * k(2)$. Replace the functions with what we know they equal to.

$2x^2+3x+8=2*16=32$

Now bring all the terms to one side:

$2x^2+3x-24=0$

Now we can solve this quadratic for $x$.

I'll put this into the quadratic formula because it cannot be factored.

$x=\frac{-b\frac{+}{-} \sqrt{b^2-4ac} }{2a}$, Compare our quadratic to the general equation of a quadratic: $ax^2+bx+c=0$.

$a=2,b=3, c=-24$

Now put these terms into the quadratic formula to get the values for $x$.

$x=\frac{-3\frac{+}{-} \sqrt{(3)^2-4(2)(-24)} }{2(2)}$

So: $x=\frac{-3+\sqrt{201} }{4}$=2.8 (1 decimal place)

or

$x=\frac{-3-\sqrt{201} }{4}$= -4.3 (1 decimal place)