# How do you find the value of c that makes #x^2+17x+c# into a perfect square?

##### 2 Answers

c = 72.25

#### Explanation:

in complete the square, we should add square of ½ of the coefficient of x to constant term.

Here 17 is the coefficient of x, ½ of 17 is 8.5 and its square is 72.25

Consider

Use the pattern

Set the middle term of the pattern equal to middle term of the given equation and then solve for c.

#### Explanation:

Set the middle term of the pattern equal to middle term of the given equation:

The first step in solving for c is to divide both sides of the equation by 2x:

The next step in solving for c is to square both sides:

This is how you find the value of c that makes the quadratic a perfect square.

Some additional information:

If the middle term of the given equation is negative, then use the pattern

Let's do an example, given

Set the middle terms equal:

Divide both sides by -2x:

Square both sides:

I hope that this helps.