Solve by completing the square:
x^2=5x+2
x^2=5x+2
x²-5x=2
x² -2(5/2)x +(5/2)²=2 +(5/2)²
The left-hand side is a perfect square:
(x-(5/2))² = 8/4 + 25/4
(x-(5/2))² = 33/4
x-5/2 = ±(√33)/2
x=5/2 ±(√33)/2
x^2=5x+2
x²-5x=2
x² -2(5/2)x +(5/2)²=2 +(5/2)²
The left-hand side is a perfect square:
(x-(5/2))² = 8/4 + 25/4
(x-(5/2))² = 33/4
x-5/2 = ±(√33)/2
x=5/2 ±(√33)/2