Question

Put the trinomial x^2+8x+14 into (x+a)^2+b form where a and b can be positive or negative. Thanks!

Answer 1

(x + a)^2 + b form can be achieved by a method known as completing the square.

Step 1: Divide the b term by 2 and square it

8 / 2 = 4

4^2 = 16

Step 2: Add and subtract 16 from the expression

---Adding 16 creates a perfect square trinomial between x^2 + 8x + 16. But, if we add 16, we also need to subtract it. So, we will subtract 16 from our c term, 14.

x^2 + 8x + 16 + 14 - 16

x^2 + 8x + 16 - 2

Step 3: Factor the perfect square trinomial

(x^2 + 8x + 16) - 2

(x + 4)(x + 4) - 2

(x + 4)^2 - 2

Answer: (x + 4)^2 - 2

Hope this helps! :)