Completing the Square Examples Page 2

Assuming the expression is a square, find c in the expression 4x² – 12x + c. What did we need to square? Don't worry, c. We're coming for you.

What can we square to find 4x² – 12x + c? We know whatever we're squaring, it will be riddled with question marks and look like

(?x + ?).

We'll need to work backwards, so turn around in your chair and bend your arms behind you. This will be tricky.

We know that the coefficient on the x term must be 2 for us to find 4x² after squaring. That's because we memorized our list of squares, thank you very much. The thing we're squaring looks like (2x + ?).

To find -12x after squaring, the product 2x(?) must be -6x. Since we're squaring, the product of the outside terms will be the same as the product of the inside terms, so each product must be half of -12x. The missing number must be -3. That's because we memorized our basic multiplication table, thank you very much. (What do you mean, we sound kind of defensive?) Time to check:

(2x – 3)² = 4x² – 12x + 9.

The coefficients on the x² and x terms work out, and now we know that c = 9. We had to square the term (2x – 3) to find it, but find it we did.