Solving Quadric Equations

Question

Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.

x^2 + 21x +__

Answer 1

We have "x² + 21x + ___"

1. To find our third term, we take the middle term's coefficient (21) and divide by 2 than square the value like this: (21/2)²
2. (21/2)² = 441/4
3. Therefore our perfect square trinomial is x² + 21x + 441/4

To write in factored form you take the middle term's coefficient (21) and divide by 2 which will produce: (x + 21/2)²

Answer 2

The number completing the square is (21/2)²