what is the value of c to make this expression a perfect square trinomial?
x^2-15x+c
take 1/2 of the coefficient of the middle term, then square it
i.e.
1/2(15) = 15/2
now we square this: (15/2)^2 = 225/4 or 56.25 in decimals
c = 225/4
To determine the value of c that will make the expression x^2 - 15x + c a perfect square trinomial, we need to complete the square.
Step 1: Take half of the coefficient of x (which is -15) and square it.
(-15/2)^2 = 225/4
Step 2: Add the result from step 1 to the expression.
x^2 - 15x + 225/4 + c
Now, if this expression is a perfect square trinomial, it can be written as the square of a binomial.
Step 3: Factor the expression.
(x - 15/2)^2 + c
To make it a perfect square trinomial, the constant term, c, should be equal to the value added in step 2. In this case, c = 225/4.
So, the value of c that will make the expression x^2 - 15x + c a perfect square trinomial is 225/4.