Question

What is the factorisation of x2+2x+4

Answer 1

If you move the 4 over, x^2+2x-4=0, you get a quadratic that does not factor. So, you have two choices here. Use the quadratic formula or complete the square.
Quadratic formula: x = (-b +- sqrt(b^2 - 4ac))/(2a) Here, a=1, b=2, c=-4.
x= (-2 +- sqrt(4-4(1)(-4))/(2*1) = (-2 +- sqrt(20))/(2) now sqrt(20) = sqrt(4)*sqrt(5) =2 * sqrt(5)
so, x = (-2 +- 2*sqrt(5))/2 now factor out a 2: 2(-1 +- sqrt(5))/2 then cancel the 2's
x = -1 +- sqrt(5)

Completing the square: x^2 + 2x = 4 half of 2 is one, square one and you get one, that is what you add to both sides: x^2 + 2x + 1 = 4 + 1
(x + 1)^2 = 5
x + 1 = +- sqrt(5)
x = -1 +- sqrt(5)
And there's your answers.