Solve each equation in Exercises 1 - 14 by factoring.

Question

6 x^{2} + 11 x - 10 = 0

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we're trying to find the value of C. In the equation 15 C squared plus 32 C minus seven is equal to zero and we're trying to solve it by fact drink. So in this case you can see that the equation follows the general form for a quadratic equation of A. X squared plus B. X Plus C is equal to zero. And when we're trying to solve by factoring we're trying to find two terms that multiply to get a time see but add to get B. So in this case or equation we can pull the values of A. B. And C. So a. is equal to 15 because it's the coefficient in front of the squared variable C squared B. Is equal to 32 because it's the coefficient in front of the C. Variable And the constant at the end is -7. So now we have our values for A. B. And C. So we want two numbers That multiply to get a times C. or in this case 15 times negative seven Which is -105. And we want to numbers to add to get B Which in this case is 32. So in this case I can try seven times or negative seven times 15 is equal to negative 105. And if I add negative seven with 15 I get negative or positive age not 32. So these are not it. If I try times negative three I get negative 105. And if I add 35 times negative or plus negative three I get 32. So I know that 35 negative three are the numbers I'm going to use. So I'm going to rewrite my equation 15 C squared. But instead of writing plus 32 C I'm going to write plus 35 C minus three C minus seven is equal to zero. So you can see that these middle terms I've just sort of separated the C. Into 35 C. And negative three C. And now I can sort of group these when I group them. I want the ratios when I divide them to be the same. So in this case if I divide x 15 I get around 2.33 i divide seven x 3 I got 2.33 as well. But I'm going to try to rearrange really quick to see if I can get a more even ratio. So that when I divide those two I can get a whole number. So I'm gonna rearrange it as 15 C squared minus three C plus 35 C minus seven is equal to zero. And now when I divide Three divided by 15 I get 1/5. And when I divide seven x 35 I get 1/5. So I'm A lot happier with this ratio because it is easier to simplify. So when I group them you can see that from this first grouping I can take out 3C and the inside becomes 5C -1. And from the second grouping I can take out seven And when I do that I'm left with five C -1. And now you can see that I have five c minus one in both of these. So I can also take that out and I'm left with five C minus one and the components left behind are three C plus seven. So now you can see that I've factored the original equation so now I can solve for each of those factors. So in one case I have five C minus one is equal to zero and in my other case I have three C plus seven is equal to zero. And from these two I can just isolate C. To try to get a value for C. So the first one I'll add one to both sides. Leaving me with five C is equal to one. I divide by five, I get C is equal to 1/5. Looking at my second factor. Also track seven from both sides leaving me with three. C is equal to negative seven, then I'll divide by three, so C is equal to negative seven divided by three. So in this case you can see that C has two answers, it could be negative 7/3 or 1/5. So that becomes my final answer and you can see that that aligns with answer choice A So hopefully this video helped and see you next time.

Solve each equation in Exercises 1 - 14 by factoring. $6 x^{2} + 11 x - 10 = 0$

Key Concepts

Factoring Quadratic Equations

Zero Product Property

Solving Linear Equations

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