If $x=2\sin\frac{3\pi}{10}$, find the value of the expression. If $x=2\sin\frac{3\pi}{10}$, find the value of the expression
$$
W =2x^5+x^4-4x^3-4x^2-x+7
$$
After a bit of thought, I got :
$$
x = \frac{\sqrt{5}+1}{2}
$$
But I don't think my teacher expected me to substitute the value of $x$ into the expression. Is there anything I'm missing ?

Use $x^2-x-1=0$. It must help:
$$2x^5+x^4-4x^3-4x^2+x+7=(x^2-x-1)(2x^3+3x^2+x)+7=7.$$
