### Video Transcript

Consider the equation 25π₯ squared minus 64 equals ππ₯ plus π times ππ₯ minus π, where π and π are constants. Which of the following could be the value of π? A) eight, B) 64, C) 25, or D) five.

If 25π₯ squared minus 64 equals ππ₯ plus π times ππ₯ minus π, we can use a square method to try and solve ππ₯ plus π times ππ₯ minus π. First, we need to multiply ππ₯ by ππ₯. This gives us π squared π₯ squared. Then, we multiply ππ₯ times π. And, we get positive πππ₯. If we multiply negative π times ππ₯, we get negative πππ₯. And, when we multiply negative π times positive π, we get negative π squared. We then need to add the four terms in the square, but positive πππ₯ plus negative πππ₯ cancels out. And so, ππ₯ plus π times ππ₯ minus π equals π squared π₯ squared minus π squared.

25π₯ squared minus 64 equals π squared π₯ squared minus π squared. Weβre interested in solving for π. But right now, we can only say that π squared equals 25. If π squared equals 25, we can take the square root of both sides, and then weβll see that π has two results. It is either positive or negative five. Out of our four answer choices, weβre only given positive five. And so, we can say that π could be equal to five.

Notice that option C is pretty close. Option C is the value of π squared. We also see that 64 as the value of π squared. And, if we take the square root of π squared and the square root of 64, weβll see that π can be positive or negative eight. So, A is a possible answer for π. 64 is equal to π squared. 25 equals π squared. And, option D, five equals π, which is what we were looking for.