# How do you find the c that makes the trinomial #x^2+9x+c# a perfect square?

##### 2 Answers

#### Explanation:

Note that:

#(x+b/2)^2 = x^2+bx+b^2/4#

So if

#c = b^2/4 = color(blue)(9)^2/4 = 81/4#

**Bonus**

More generally, we find:

#ax^2+bx+c = a(x+b/(2a))^2+(c-b^2/(4a))#

which if

#x^2+bx+c = (x+b/2)^2+(c-b^2/4)#

as in our example.

The pattern is:

Match the terms of the given equation with the right side of the pattern.

#### Explanation:

Match the terms of the given equation,

Matching the first terms:

Matching the second terms gives us the following equation:

We can use the above equation to solve for the value of "a" by dividing both sides of the equation by 2x:

Matching the constant terms, gives us the following equation:

Substitute

This is your answer: