Question

What number must you add to complete the square x^2-20x=17

Answer 1

$(*)\ (a-b)^2=a^2-2ab+b^2$

$x^2-20x=17\\\\x^2-2\cdot x\cdot10=17\ \ \ |+10^2\\\\\underbrace{x^2-2\cdot x\cdot10+10^2}_{(*)}=17+10^2\\\\(x-10)^2=117$

Answer: 10² = 100