Solve each equation in Exercises 1 - 14 by factoring.

Question

x^{2} = 8 x - 15

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we're trying to get the value of A. In the equation a squared is equal to two A plus 1 68. And we're trying to get the value of A. By factoring so in this case our first step to be able to factor is to get all the terms on one side. So you can see right now we have a squared on the left hand side and two A plus 168 on the right hand side. So I'm gonna go ahead and move the to A. In the 168 over two The left side by subtracting two a. and 168 from both sides. So that leaves me with a squared minus two A minus 1 is equal to zero. And now I have this equation A squared minus two a minus 68. And you can see that it follows the form of a quadratic equation where the general form of a quadratic equation is x squared A. X squared plus bx plus C is equal to zero. And when we're factoring a quadratic equation, we want two terms that multiply to get a times C. But when those two terms are added, you got B. So we're gonna try to use this general form to help us factor our equation. So in this case you can see that A. is equal to one and perhaps it's a little bit confusing because in the journal form of the quadratic equation, the variable is represented by X. So keep in mind that our equation A. Is equal to X. Because in our equation A. Is the variable. And we're looking at the coefficient in front of the variable squared, which in this case is one and C. Is equal to the constant at the end. So negative 1 68 and B is equal to the coefficient in front of the variable not squared. And in this case that's negative two. So now you can see that we want two numbers that multiply To get negative 1 68 or eight times c. And add To get -2. So we can start looking at the factors of -168. So in this case if I try -12 and 14, Those multiplied together give me -168. And if I add negative 12 and 14 I'm left with positive too. So I know that I need to switch the signs on these so 14 needs to be negative and 12 positive. And now if I multiply 12 times negative 14 I still have negative 168. And when I add 12 with negative 14 I'm left with negative two. So I know that 12 and 14 are going to be my two factors. So in this case I can rewrite my factors as a plus 12 Times A -14 Equal to zero. So now you can see that I've Factored my original equation and I'm left with these two terms a plus 12 and a -14. So using these two terms, I can figure out the values of a. So on one hand I have a plus 12 is equal to zero. And on the other hand I have a minus 14 is equal to zero. And in order to solve for a I just need to isolate A. On one side. So looking at my first factor, I just need to subtract 12. Leaving me with a is equal to negative 12. And looking at my second factor, I need to add 14. So if I add 14 I'm left with a. is equal to positive 14. So you can see that they could be two values negative 12 or 14. And that becomes my final answer for the value of A. And you can see that that aligns with answer choice D. You see all these answers are the same. But the negative signs are applied to different numbers. So whenever you're choosing an answer, be careful of making sure that the signs align but hopefully this video hoped and see you next time

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

Key Concepts

Rearranging Equations to Standard Form

Factoring Quadratic Expressions

Zero Product Property

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