Question

What are the exact solutions of x2 = 5x + 2?

Answer 1

\[x ^{2}-5x-2=0\]
\[(-5)^{2}\pm \sqrt{(-5)^{2}-4(1)(-2)}/2\]
\[(25\pm \sqrt{25+8})/2\]
\[(25\pm \sqrt{33})/2\]
So, the 2 exact solutions would be,
\[(25+\sqrt{33})/2; (25-\sqrt{33})/2\]
Alternatively, you can take square root of 33, so:
\[(25+ 5.74)/2 ; (25-5.74)/2\]
\[30.74/2 ; 19.26/2\]

Final solutions are: 15.37 and 9.63