Complete the expression nine 𝑥 squared blank plus 144 to make a perfect square.
In order to make a perfect square, the middle term needs to be equal to plus or minus two times the square root of the first term times the square root of the third term. Our first term is nine 𝑥 squared. And our third term is 144. So let’s go ahead and plug these in. That way, we can find our missing middle term.
So we have plus or minus two times the square root of nine 𝑥 squared times the square root of 144. The square root of nine is three. And the square root of 𝑥 squared is 𝑥. And now the square root of 144 is 12. So we have two times three 𝑥 times 12. And when multiplied together, we get plus or minus 72𝑥. Therefore, to complete this expression, to make it a perfect square, we would need either 72𝑥 or negative 72𝑥.