### Video Transcript

Find the real values of π₯ and π¦ that satisfy the equation π₯ plus π¦π equals 10 plus four π squared.

If we get a complex number into the form π plus ππ, π and π are real numbers. And for us, that means here both π₯ and π¦ are real numbers. We have to take 10 plus four π squared and put it into the format of π plus ππ.

At first glance, you might be tempted to take the square root of both sides. However, once weβre here, we end up with a whole host of other problems and weβre no closer to the format π plus ππ. Instead of doing that, we want to actually square 10 plus four π.

We want to find out what 10 plus four π times 10 plus four π is. We can FOIL these two terms. 10 times 10 equals 100. 10 times four π equals 40π. Four π times 10 equals 40π. And four π times four π equals 16, four times four equals 16, π squared, π times π equals π squared.

We combine our like terms. And now, our equation says π₯ plus π¦π equals 100 plus 80π plus 16π squared. You have to remember that the imaginary number π is equal to the square root of negative one. π squared equals the square root of negative one squared, negative one. π squared equals negative one.

In our equation, in place of π squared, we substitute negative one. And then, we have 16 times negative one equals negative 16. 100 plus 80π minus 16. We can combine 100 and negative 16 to get 84 plus 80π. Now, our equation is in the correct format π₯ plus π¦π equals 84 plus 80π. π₯ equals 84 and π¦ equals 80.

The real values for π₯ and π¦ are 84 and 80.