Question
In Exercises $35-46,$ determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.$$x^{2}-14 x$$
In Exercises $35-46,$ determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-14 x $$
Answers
Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}-14 x $$
X squared plus 14 axe. How do we turn this into a perfect square? Try no me. When we take that middle coefficient 14 we cut it in half and then we square it. So seven squared is 49. If we add 49 to the expression, then we'll have a perfect square shrine oatmeal.
And this a question. It's required toe. Add a number constant number. Do this by an army under tow. Get a perfect square through not Jenna Me, which has de factor in term. Inform off X plus a number, see to the power off too. So how to get this number as to take the coverage it off X which is here One dividing number by two. Then dick the in this number and quality power off too. So it is one over to the board of two is one over four. So this is the number that should be added to the ah by another in order to get the perfect square through an army went over four and the the ah factor off this specific square paranormal is X Ah, plus the number here, which is one over two. The gulf it off X divided by two, which is one over two Did the hole is too far off to So this is the factor off this stray normal
Welcome. We're here today to determine what number must be added to our given expression into this blank space To make it a perfect square. Try No, me. As you know, this is essentially the process of completing the square. So with any given, um quadratic or relative quadratic where you're about to form it, you have the standard e standard form of a X squared plus B x plus B x plus. See, so relating that to our equation. Over here, we know that a equals one a equals one b equals 14 and we are trying to determine what C equals to make it a perfect square tryingto make. So to do that, we must, um, essentially take half of our be term. So solving that so half of RB term is going to be 14 divided by two, which equals seven. And then you want to square that so seven squared is gonna equal 49 49. And that is what you add to your expression. To make it a perfect square, try no meal. So adding 49 for expression we get X squared. X squared plus 14 x was 14 x plus 49 49 and then rewriting it to make it a little bit simpler. Weakened right X plus seven squared experts. Seven squared. All right, so in the end, we added 49 2 r expression to make it a perfect square. Try no meal. I hope this hopes and keep at the great work.
We're being asked a factor. The given perfect where? China meal And we know it's a perfect square triangle meal because both the first and last terms are perfect words, and our middle term is the product of those square roots. So when we factor this, we're going to have one binomial that's going to get square To get the first term. We simply take the square root of the first term and the square. The Vex squared is just acts since X Times X is X squared, the second term is going to be the square root of the last term in our China meal and the square of the 49 7 since seven times seven is 49. Now for our sign, because the sign of the middle term is negative are sign will also be negative. So our final factor that