Solve f(g(x))=30 with nested functions and factor an expression

[Nikola Tesla]

If f(x)=x^2-3x and g(x)=in square root of x+6, solve for x if f(g{x))=30

Also, factor this expression and simplify if necessary: (x+5)^2+6(x+5)(x-4)

Thanks.

 

[d_leet]

What have you tried so far? What are you having trouble with?

 

[Nikola Tesla]

For the first one, I got to, x+6 - 3(square root of x+6) = 30 lol

I don't know what to do next, I think I'm supposed to get rid of the three, but I'm not sure how.

 

[d_leet]

For the first one, I got to, x+6 - 3(square root of x+6) = 30 lol

I don't know what to do next, I think I'm supposed to get rid of the three, but I'm not sure how.

You can make a substitution to end up with a quadratic equation,

let u = square root of (x+6)

so you end up with

u² - 3u = 30

You can then solve for u and thn substitue back to solve for x.

 

[VietDao29]

Also, factor this expression and simplify if necessary: (x+5)^2+6(x+5)(x-4)

For the second one, you may want to factor (x + 5) out.
(x + 5)² + 6(x + 5)(x - 4) = (x + 5) (x + 5 + 6(x - 4)) = ...
Can you go from here? :)