In Exercises 35–46, determine the constant that should be added t...

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 - 10x

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to complete the square for the equation M squared minus 18 M. And in this case it's important to remember that when you're working with a binomial as a form X squared plus bx and you complete the square by adding B divided by two squared. So in this case our equation m squared minus 18 X. Or 18 M follows that binomial form where B Is equal to -18. So we're gonna be adding -18, divided by two squared or negative nine Squared. Which negative nine times negative nine is positive 81. So we're actually going to be adding 81. So if we do that we have M squared minus 18 M plus 81. And in this case you can see that we added an 81 into our equation. So in order to not change the value of the equation, we have to make sure that wherever we add something we subtracted. So we've added 81 inside and I'm going to group that with the M squared minus 18 M. But I still need to subtract 81 because I can't just add Random numbers. So now you can see that plus 81 and -81 equate to zero. So it's like I've added nothing to my equation. So I don't change the value of it but I've completed this square. So in this case I can now factor out M squared minus 18 M plus 81 it becomes m minus nine squared And I still have the -81. So in this case you can see that m minus nine times m minus nine will give me m squared minus nine m minus nine And - times -9 is positive 81. So M squared minus 18 M plus 81. So you can see that I completed the square correctly because when I multiply m minus nine times and minus nine I get my original equation M squared minus 18 M plus 81 back. So this becomes my final equation. And you can see that the answer choices are all very similar and we know that the 81 on the outside has to be negative because we added 81 on the inside. So we know that answer choice C. And D. Are wrong. And then it comes down to whether or not the m minus nine is minus nine or plus nine and we determined that it was negative nine. So answer choice A is the correct answer. And if we had worked out um plus nine times M plus nine we would get M squared. Sometimes I'm is I'm squared M times nine is nine M nine times M is nine M nine times nine is 81. So we'd be left with M squared plus 18 M plus And notice how this 18 is positive. Well this 18 is negative so we want that minus so just to confirm that our answer is in fact a so hopefully this video helped and see you next time.

Struggling with College Algebra?

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 - 10x

Watch next

The Square Root Property practice set