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VashaNatasha [74]
1 year ago
13

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

Mathematics
1 answer:
Sav [38]1 year ago
4 0

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

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 <u>a = x, and b² = c</u>, but we need to find the numerical value of c.

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

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

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