Question 44416
{{{x + sqrt(31-9x) = 5}}} 
Rearrang so the square root is the only term on the right hand side:
{{{5-xsqrt(31-9x)}}}
Now square both sides:
{{{(5-x)^2=31-9x}}}
Use FOIL to expand the left hand side:
{{{25-10x+x^2=31-9x}}}
Rearrange to give a quadratic expression with zero on the right hand side:
{{{x^2-10x+9x+25-31=0}}}
{{{x^2-x-6=0}}}
Factorise:
{{{(x+2)(x-3)=0}}}
So  the solutions are x=-2 or x=3.
I have plotted the curve {{{y=x + sqrt(31-9x)}}} and the line {{{y=5}}} Below. Note thet the solutions occur when the red line intersects the green line, when x=-2 and when x=3. This proves The solutions are accurate.

{{{ graph( 300, 200, -3, 3.4, -1, 6, x + sqrt(31-9x), 5) }}} 

I hope this helps.
I am currently constructing my own homework help website, and would greatly appreciate any feedback on the help you recieved to my email address: adam.chapman@student.manchester.ac.uk

Adam