Question

Solve for x in the equation x2-8x+41=0

Answer 1

$x^2-8x+41=0\ \ \ \ |-41\\\\x^2-2\cdot x\cdot4=-41\ \ \ \ |+4^2\\\\\underbrace{x^2-2\cdot x\cdot4+4^2}_{(a-b)^2=a^2-2ab+b^2}=-41+4^2\\\\(x-4)^2=-41+16\\\\(x-4)^2=-25 < 0$

Answer: No real solutions