Question

Is this a trinomial square? x^2+3x+4

Someone wanna teach me how to do this?

Answer 1

@iGreen

Answer 2

If you have x^2 + bx + c, then to complete the square, you take the coefficient of x, which is 'b' here, divide it by 2.
Then rewrite the original equation as: (x + b/2)^2 - (b/2)^2 + c and simplify. This would complete the square. If it is a perfect square, then it would simplify to just (x+b/2)^2. If not it is not a square.

x^2-5x+25 = (x - 5/2)^2 - (5/2)^2 + 25 = (x - 5/2)^2 - 25/4 + 25 =
(x - 5/2)^2 + 75/4.
This is NOT a perfect square.