x^2 + bx + c = 0

Question

I need to know how to do this math question,

Answer 1

Let x²+bx+c=0,

x²+bx=-c, complete the square:

x²+bx+b²/4=b²/4-c,

(x+b/2)²=b²/4-c=(b²-4c)/4,

(x+b/2)²-(b²-4c)/4=0, difference of two squares:

(x+b/2+√(b²-4c)/2)(x+b/2-√(b²-4c)/2)=0.

So x²+bx+c=(x+b/2+√(b²-4c)/2)(x+b/2-√(b²-4c)/2) when factorised.