In Exercises 64–65, determine the constant that should be added t...

Question

In Exercises 64–65, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2+ 20x

Accepted Answer

Hello. Today we're going to be turning a binomial into a factory trim a meal and identifying what number makes this a factory will try no meal. So the binomial is X squared minus nine X. So how can we figure out what number can turn this into a fact? Herbal try no meal while there is one process that helps us with that and it's called completing the square, completing the square. So what is completing the square ST well completing the square states that if we have a binomial in the form of eight X squared plus Bx then we can go ahead and add a number C. Which is equal to B divided by two. That quantity square and adding that C. Is going to turn this into a fact herbal try no meal. So we're gonna go ahead and use this process to identify what number makes this fact arable. So we need to first identify what our B term is. Our B term is just the coefficient in front of our X. Term. In this case it's going to be negative nine. So B. Is equal to negative nine. Now, what we're gonna do is figure out our number C. C. Is going to equal to negative nine divided by two squared. Now negative nine is not divisible by two. So in order to square this quantity we're just gonna apply the square to both the numerator and the denominator. Doing so is going to give me negative nine squared over two squared. Now negative nine squared is gonna be positive 81 2 squared is going to be four. So we're gonna go ahead and add 81/4 to this binomial. In order to make this a fact. Herbal try no meal now we need to go ahead and factor this binomial. Well in order to factor this, try no meal, we need to think of two numbers that can multiply together to give us positive 81/ and add up to give us negative nine. Well those two numbers are going to be negative 9/2. So let's go ahead and multiply negative 9/2 together to double check this negative 9/2 times negative 9/2 is gonna give me positive 81/2 which is the last term. And adding negative 9/2 To negative 9/ is going to give me negative 18/2 which is equal to negative nine and that satisfies, satisfies our middle term. So that means that this tree no meal is going to factor two x minus 9/2 squared and that's gonna be our second part of the solution. So in total the term that made this fact, Herbal is 81/4. And after factoring we are left with x minus 9/2 squared, that means that the solution to this equation or the solution to this problem is going to be D. So I hope this helps you understand on how to use completing the square and I'll see you all in the next video.

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