Solve each equation in Exercises 1 - 14 by factoring.

x^2 = 8x -...

Question

Solve each equation in Exercises 1 - 14 by factoring.

x^2 = 8x - 15

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to solve for a and the equation a squared is equal to two a plus 168. So in this case we want to try to solve by factoring which means I want to move all my terms to one side. So right now I have a squared is equal to two a plus 168 and I'll move everything to the left. So also tracked to a 168 from both sides. So that leaves me with a squared -2. A -168 is equal to zero. And in this case because I'm trying to solve by factoring I need to find two terms that when I multiply the first component together I get a squirt. So if I multiply eight times eight I would get a squared. So keep those terms first. And when I multiply the second terms they need to multiply to give me -168 but add to give me -2. So they need to multiply to 168 because that's my last term. But they need to add to negative two because that's my middle term. So I can try negative times positive 14 gives me negative 168. And if I try adding those negative 12 plus positive gives me positive two. So if I switch the sign you can see that when I multiply 12 times negative 14 I still get 100 negative 168. And now when I add 12 with negative 14, I get negative two. So 12 and negative 14 are my two factors. And we can also check this. You can see that when I multiply this again, I have a squared minus 14, A plus 12, a minus 168. If I combine the middle terms I have a squared minus two a minus 168 and I get back my original equation. So know that this Factory ization is good. I'll make it more clear that this is -14 and because this is equal to zero, I can solve these separately where I have a plus 12 is equal to zero and A -14 is equal to zero To solve for a. I'll subtract 12 from both sides. So it tells me a is equal to negative 12 And I'll do the same for the second equation. I'll add 14 to both sides. So it leaves me with a is equal to positive 14. You can see I have two solutions for a so a could be negative 12 or positive 14. So this becomes my final answer for this equation and you can see the answer choice. D also has negative 12 and positive 14. So hopefully this video helped and see you next time

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Solve each equation in Exercises 1 - 14 by factoring. x^2 = 8x - 15