Question: What value of c will complete the square below ([tex]x^{2} +30x+c[/tex]) and make the expression a perfect square trinomial?
Answer: c = 225
Step-by-step 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 [tex]c[/tex].
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 [tex]2x[/tex] 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.)
