Solve each equation in Exercises 1 - 14 by factoring.

Question

3 x^{2} - 2 x = 8

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where I'm trying to find a value of J. In the equation to j squared minus 13 J equals we want to try to solve by factoring so in this case you can see that I have terms on both the left hand side and the right hand side of the equal sign. So in order to factor I'm going to get all my terms on one side. So I can lend factor that new equation. So I'm gonna move the 45 over by subtracting By 45 on both sides. So my left hand side becomes to J squared minus 13 J minus 45. And my right hand side is now equal to zero. So now I have all of my terms on the left hand side and you can see that the left hand side follows the quadratic equation form or I have a X. Squared plus bx plus C. And when I'm factoring a quadratic equation that follows the form I want my two numbers to multiply to get a C and add to get B. So I'm gonna use this general form to try to help me find my factor terms. So in this case eight times c. is equal to two times negative or negative 90. So I want terms that multiply to negative 90 but add to my B. Value Where B. is equal to -13. So if I try negative nine and 10 if I add those together I get one If I do positive nine and negative 10 I get -9, not negative 13. So I know that these two factors are not it. If I try five and 18 I have positive 18 and negative five multiplied together. I get negative 90. But if I add those together I get positive 13. So if I switch the sign So I have positive five and negative Multiplied together, I get negative 90 and added together I get negative 13. So I know that these are the two numbers that I want to use. So in this case I'm going to rewrite my equation replacing the middle term using the -18 and the positive five. So my equation becomes two J squared minus 18, J Plus five, J -45. So notice how negative 18 J and Positive five. Gray still equate two negative 13. So I haven't changed anything In these two sets of equations. So now I'm going to Factor out these two and I'm going to factor them out sort of separating this equation And to so I have this first set to j squared minus 18 J and I'll have this second set five J minus 45. This is known as factoring by grouping. So in this case, in this first set I can take out to J and if I do that, my first term becomes J because two J times J is the same as two J squared And my second term becomes nine because 18 -18 J divided by two J is -9. And I can do the same to my second set where I can take out five and I'm left with five. J divided by five is J. And -45 divided by five is negative night. So now notice that I have J -9 on both of these. So I can go ahead and take that out. And if I do that I'm left with to J and positive five. So now you can see that I have these two factor terms for J and I can set them equal 20 because remember that I moved all my terms to one side. So the other side is equal to zero and I can solve for J. And if I do that I have J -9 is equal to 0-plus nine. I got J is equal to nine and I have two, J plus five is equal to zero -5 -5. I'm left with two. J is equal to negative five. If I divide by two, I have J is equal to negative five. House. So here you can see that I have these two values for J. Where J could be positive nine Or -5/2. So this becomes my final answer for jay from the equation to j squared minus 13. J is equal to 45 and you can see that this aligns with answer choice C. So these other answer choices have very similar answers. Just some of the signs are switched and some of the numbers are switched on the fractions, so when you're choosing an answer, be very careful. But hopefully this video helped and see you next time.

Solve each equation in Exercises 1 - 14 by factoring. $3 x^{2} - 2 x = 8$

Key Concepts

Rearranging Equations to Standard Form

Factoring Quadratic Expressions

Zero Product Property

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