FIND THE VALUE OF K, SO THAT THE EXPRESSION IS A PERFECT SQUARE TRINOMIAL.

x^2+6x+k

k=

k=9

find half of 6x then square it

To find the value of k so that the expression x^2 + 6x + k is a perfect square trinomial, we need to use the following formula:

a^2 + 2ab + b^2 = (a + b)^2

In this case, a is the square root of x^2, which is x. And b is half the coefficient of x, which is 6/2 = 3.

So, we will have:

x^2 + 2(x)(3) + 3^2

= x^2 + 6x + 9

To make the expression x^2 + 6x + k a perfect square trinomial, we need to set k = 9.

Therefore, k = 9.

To find the value of k such that the expression x^2 + 6x + k is a perfect square trinomial, we need to complete the square.

A perfect square trinomial can be expressed as the square of a binomial, meaning it can be factored into the form (x + a)^2, where a is a constant.

To get the quadratic expression in the form of a perfect square trinomial, we need to add and subtract a suitable constant to the expression x^2 + 6x + k.

To determine this constant, we take half of the coefficient of x (which is 6) and square it. In this case, (6/2)^2 = 9.

So, to express x^2 + 6x + k as a perfect square trinomial, we add and subtract 9 to the expression:

x^2 + 6x + 9 - 9 + k

Rearranging this, we have:

(x^2 + 6x + 9) + (k - 9)

The expression in parentheses is a perfect square trinomial, specifically (x + 3)^2.

Therefore, the expression x^2 + 6x + k can be rewritten as (x + 3)^2 + (k - 9).

For this to be a perfect square trinomial, the constant term (k - 9) must be zero since adding zero to a perfect square trinomial does not change it.

Therefore, k - 9 = 0, which implies k = 9.

So, the value of k that makes the expression x^2 + 6x + k a perfect square trinomial is k = 9.