Question

What value of cc​ will complete the square below and make the expression a perfect square trinomial?

x^2+30x+c

Enter the perfect square trinomial as a squared binomial.

Answer 1

Question: What value of c​ will complete the square below (
`x^(2) +30x+c`) and make the expression a perfect square trinomial?

Answer: c = 225

Explanation:

Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)². In the presented trinomial, we can immediately identify that a = x, and b² = c, but we need to find the numerical value of
`c`.

To do this, note that the middle term, or 2ab, corresponds with (is equal to) 30x. We know that a = x, and thus, 2ab = 2bx. Now, 2bx and 30x are corresponding terms; thus, 2bx = 30x.

Dividing by
`2x` on both sides gives us b = 15. Therefore, c = b² = 15² = 225. (As a squared binomial, this would be (x + 15)² as a = x and b = 15.)