# Question Video: Manipulating Quadratic Expressions by Completing the Square Mathematics • 9th Grade

Given that 3π₯Β² + 3π₯ + 5 = π(π₯ + π)Β² + π, what are the values of π, π, and π?

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### Video Transcript

Given that three π₯ squared plus three π₯ plus five is equal to π times π₯ plus π squared plus π, what are the values of π, π, and π?

Essentially, we need to take our function and complete the square. So the first thing that we need to do is to group the first two terms together, and now take out a greatest common factor, excluding the variables.

And now our goal is to turn this into something that is squared, so we need to make this a trinomial. So the first thing that we need to do is to take π over two and square it. And in this case, π is one, and one-half squared is one-fourth. So we can plug in one-fourth.

However, we canβt just add a number to our function. So if weβre adding one-fourth, we need to subtract it from the end. However, that isnβt actually a one-fourth; that is actually a value of three times one-fourth, which is three-fourths. So we need to subtract three-fourths from the edge, so we have three times π₯ squared plus π₯ plus one-fourth plus.

To add our fractions, I need to have a common denominator. And five is the same as 20 over four, so twenty-fourths minus three-fourths is equal to seventeen-fourths.

Now like we said before, we wanted whatβs in the parentheses to be something squared, and it is. That is actually equal to π₯ plus one-half squared, because one-half times one-half is equal to one-fourth, and then we add one-half and one-half together; we get one. So π is one and π is the one-fourth.

So if this is equal to π times π₯ plus π squared plus π, π would be three, π would be one-half, and π would be seventeen-fourths. So again, π equals three, π equals one-half, and π equals seventeen-fourths.