Question

PLEASE HELP

Given:
g(x) = 2x2 + 3x + 8
k(x) = 2x + 12
Solve the equation g(x) = 2k(2) algebraically for x, to the nearest tenth. Explain why you chose the method
you used to solve this quadratic equation.

Answer 1

`x= 2.8`

or

`x=-4.3`

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

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=(-b(+)/(-) √(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=(-3(+)/(-) √((3)^2-4(2)(-24)) )/(2(2))`

So:
`x=(-3+√(201) )/(4)`=2.8 (1 decimal place)

or

`x=(-3-√(201) )/(4)`= -4.3 (1 decimal place)