### Video Transcript

Solve the equation ๐ฅ squared minus 14 ๐ฅ plus 38 is equal to zero by completing the square.

This question has asked us to solve the equation by completing the square. So what Iโm gonna do is Iโm going to recap that first. So the general rule if we have our expression in the form ๐ฅ squared plus ๐๐ฅ is that this is equal to ๐ฅ plus ๐ over two all squared โ and thatโs because weโve actually halved the coefficient of ๐ฅ โ and then minus ๐ over two โ again halving the coefficient of ๐ฅ โ and that is all squared.

So if we look back to our equation, we can actually see that itโs the first two terms that are actually gonna apply to completing the square rule too. And these two terms are ๐ฅ squared minus 14๐ฅ. So if we actually apply this and complete the square of our first two terms, weโre gonna get ๐ฅ plus and then weโve got negative 14 over two because a coefficient of our ๐ฅ is negative 14 and thatโs all squared and then minus again negative 14 over two all squared. Then we still have plus 38 is equal to zero.

Okay, we can tidy this up. So we get ๐ฅ minus seven all squared and itโs ๐ฅ minus seven because we had ๐ฅ plus and then negative 14 over two. Well, negative 14 over two is negative seven. So if you add a negative, itโs the same as just subtracting it. And then minus 49. And we get that again because we had negative seven all squared. If you square a negative, we get a positive. And then add 38 is equal to zero. So then if we simplify, we get ๐ฅ minus seven all squared minus 11 is equal to zero.

And then our next stage is to actually add 11 to each side of the equation, which gives us ๐ฅ minus seven all squared is equal to 11. And then if we take the square root of each side, we get ๐ฅ minus seven is equal to plus or minus the square root of 11.

And now into our final stage, which is actually going to be letโs add seven to each side of the equation. So then, weโre left with ๐ฅ is equal to seven plus or minus root 11. So therefore, the solutions to the equation ๐ฅ squared minus 14๐ฅ plus 38 equals zero are ๐ฅ is equal to seven plus root 11 or ๐ฅ is equal to seven minus root 11. And we found these by completing the square.