Find C to form completing Square x^(2) +5x + C

Question

Find C to form completing Square

`x^(2) +5x + C`

Answer 1

`(25)/(4)` (or 6.25)

Explanation:

Let's do a simple square problem to see the relationship between the elements of the resulting equation...

`(x+3)(x+3) = x(x+3) + 3(x+3) = x^(2) +3x + 3x + 9 = x^(2) + 6x + 9`

As you see, the number of 'x' (6) is the double of the numeric part of the binomial expression (3), while the numeric-only part (9) is the square of the numeric part of the binomial expression (3).

So, if we look at the formula from the problem, we see the the number of 'x' is 5. To obtain the C value, we need to divide the 5 by 2... then get the square value of the result.

`(5)/(2) * (5)/(2) = (25)/(4)` (or 6.25)