Solve each equation using the quadratic formula. See Examples ...

Question

Solve each equation using the quadratic formula. See Examples 5 and 6.

$(3 x + 2) (x - 1) = 3 x$

Accepted Answer

Hello, everyone. We're going to use the quadratic formula to find X in the equation 11 X plus two times X minus 17 equals seven X. So I recall that to use the quadratic formula, I need my equation to equal to zero before I can make this equation equal to zero. I need to multiply out those by no meals. So first thing I'm gonna do is foil. So first we'll give me 11 x squared outer will give me negative 187 X inner positive two X and last a negative for still equal to seven X. So combining my like terms, I have 11 X squared -185 x - equals seven X. And I'm going to subtract seven X from both sides. So I get 11 X squared -192 x -34 equal zero. So now that I have this set up so that it is equal to zero, I need to recall the quadratic formula. So the quadratic formula works when we have things that are set up as A X squared plus B X Plus C equals zero. So for our equation a is going to be B is going to be a negative 192 And C is going to be -34. And then the entire formula is that X equals negative B plus or minus the square root of B squared minus four A C all over two A. So we're gonna plug these values in and I'm going to come over here a little bit just so I have some space. So X equals negative B which is the opposite of B. So the opposite of negative 192 is plus or minus the square root of negative squared. I look forward to that number minus four times A which is 11 times C which is negative All of it over to a. So two times 11, we're gonna have some big numbers in this one. So let's see what we can multiply through. So X equals 192 plus or minus the square root of negative 192 squared. So let's see what that is. And I have that as 36864 And then I need to do -4 times times a negative 34 And that's gonna give me a positive And all of that's going to be over two times 11 which is 22. Alright. So now let's add up what's under the radical. So we have 192 plus or minus the square root Of 3000, sorry, 36,864 plus 1,496, which is 38,360. All of that over 22. Alright. So I don't want to leave this answer is this and based on looking at our solutions that are options for answer choices, I'm going to say this can be simplified a little bit. I'm going to off to the side try to simplify the square root of 38,360. Just because if I can simplify that I can reduce the rest of the fraction. So I don't think that's a perfect square. I do think if nothing else we can factor a four. So the square to four times 9000 will break this down. And when we do that, the square to four is two, so we end up with two Times a squared of 9590. So we're gonna go plug that right back into our quadratic formula. So x over here is going to equal 192 plus or -2 times the square root of over 22. And now every single one of my terms can be reduced by two. So when we do that, we get x equals half of 192 is 96 plus or minus. We're gonna cancel the two off the front of the radical. So the square root of over 11. So this will be our solution. We do need to break it into two pieces for it to match our answer choices. So when we break it into two pieces, This would be, and I'm just going to drag it right over here. The x equals 96 plus the square root of 9590 over And X would equal 96 - the square root of 9590 over 11. So now matching that up with our answer choices, it appears to be answer choice. A have a nice day.

Solve each equation using the quadratic formula. See Examples 5 and 6.
$(3 x + 2) (x - 1) = 3 x$

Key Concepts

Quadratic Equations

Expanding and Simplifying Expressions

Quadratic Formula

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