1. Solve for X(2)

$\displaystyle 0=-\frac{\sqrt{x+2}(x-7)}{2}+12$

2. Originally Posted by Punch
$\displaystyle 0=-\frac{\sqrt{x+2}(x-7)}{2}+12$
The method here is the same as before. If we multiply by 2 throughout:

Again $\displaystyle x > -2$

$\displaystyle 0 = -(x-7)\sqrt{x+2} + 24$

$\displaystyle (x-7)\sqrt{x+2} = 24$

square both sides

$\displaystyle (x-7)^2(\sqrt{x+2})^2 = 24^2$

Simplify and solve for x. Remember to check for extraneous solutions

3. I did it like this, however won't we get a power of 3 when we expand?

4. Originally Posted by Punch
I did it like this, however won't we get a power of 3 when we expand?
Yep

(x-7)^2(x+2)

(x+2)(x^2-14x+49) = x^3-14x^2+49x+2x^2-28x+98

Collect like terms: x^3-12x^2+21x+98

x^3-12x^2+21x-478=0

Solve for x, very tricky: http://www.wolframalpha.com/input/?i=x^3-12x^2%2B21x-478%3D0

5. For general solution of the cubic, you might Google "Cardano". The history is interesting also.

6. Originally Posted by e^(i*pi)
The method here is the same as before. If we multiply by 2 throughout:

Again $\displaystyle x > -2$

$\displaystyle 0 = -(x-7)\sqrt{x+2} + 24$

$\displaystyle (x-7)\sqrt{x+2} = 24$

square both sides

$\displaystyle (x-7)^2(\sqrt{x+2})^2 = 24^2$

Simplify and solve for x. Remember to check for extraneous solutions
Just a correction.
here $\displaystyle x \geq -2$