To determine the value of c that makes the expression x² + 7x + c + 49 – 4 – 7 – 2 – 7 – 2 – 49 – 4 into a perfect square trinomial, we first need to understand the basis of a perfect square trinomial.
A perfect square trinomial takes the form (a + b)² or (a – b)², which expands to a² + 2ab + b². In our case, we can rewrite our expression as follows:
- Combine constants:
c + 49 – 4 – 7 – 2 – 7 – 2 – 49 – 4 = c – 24
The expression will become a perfect square trinomial if we can express it as (x + 3.5)² since the coefficient of x is 7. This means:
- 0 = x² + 7x + 12.25 ; where 12.25 is also 49 / 4.
- If we set c – 24 = 12.25, we can solve for c:
c – 24 = 12.25
c = 12.25 + 24
c = 36.25
Thus, the value for c that will create a perfect square trinomial from our expression is 36.25.