So, what level of calculator is allowed at this tournament? If graphing, use the graph to demonstrate there is only one real solution and the numeric solver to find that solution. If scientific, you face the problem of finding the Lambert W function on a scientific calculator.
W(ln3/2)≈.3768
=>m^2= (e^>.3768)^2≈ 2.125=>x=3+m^2;=>x≈5.125
So, what level of calculator is allowed at this tournament? If graphing, use the graph to demonstrate there is only one real solution and the numeric solver to find that solution. If scientific, you face the problem of finding the Lambert W function on a scientific calculator.
x = 3 + exp(2W(ln(3)/2))
let u^2=x-3 , (u^2)^(u)=3 , W(ln3/2)=W(lnu*e^(lnu)) , u=e^(W(ln3/2)) , x=u^2+3 , test , OK ,