Solve each equation. -2x² +11x = -21

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Hello, today we're going to be solving the following quadratic equation. So what we are given is negative three X squared plus five X is equal to negative 22. Now, since we want to solve for X, we want to set this equation equal to zero. And in order to do that, we're going to add 22 to both sides of this equation. So what we have is negative three X squared plus five X plus 22 is equal to zero. And we want this leading coefficient to be positive. So in order to do that, we're going to have to divide everything by negative one and that is going to give us three X squared plus five. I'm sorry, not plus five X minus five X because we're dividing it by negative one -22 is equal to zero. And we can go ahead and solve this by using the quadratic equation. The quadratic equation states that X is going to equal to negative B plus or minus the square root of B squared minus four times A times C all over two times A. And this is where A B and C are going to be the coefficients of the trine Amiel. So here the coefficient of the first term of this equation is three. So we're going to let a equal to three, the coefficient of the second term is negative five. So B is equal to negative five and the constant is going to be negative 22. So C is equal to negative 22. So if we plug this into the quadratic equation, what we have is X is equal to negative B which is going to be negative negative five. So that's going to give us positive five plus or minus the square root of B squared, which is negative five squared minus four times A which is three times C which is negative 22 all divided By two A which is going to be two times 3. Now, simplifying the numerator negative five squared is going to give us positive 25 and negative four times three times negative 22 Is going to give us positive 264. So what we have is five plus or minus the square root of 25 plus 264 divided by two times three, which is going to be six and 264 plus 25 is going to give us 289. So we have X is equal to five plus or minus the square root of 289 divided by six. Now, the square root of 289 is going to simplify to give us 17. So we have X is equal to five plus or minus divided by six. And since this is a plus and minus statement, we can separate this into two equations, we get X is equal to five plus 17 divided by six. And we get X is equal to five minus 17 divided by six. So on the left hand side, 17 plus five is going to give us 22 dividing that by six. Well, actually, that can't be simplified. So we're gonna leave it as 22/6 And we can go ahead and simplify this by dividing both the numerator and denominator by two. And that is going to give us 11/3, which is going to be the first solution for X. Now, on the right hand side 5 -17 is going to give us -12. And what we have is negative 12 divided by six, which is going to give us -2. And that is going to be the second solution for X. So in total, we have two real solutions for X X is equal to negative two and X is equal to 11/3. With that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Solve each equation. -2x² +11x = -21

Key Concepts

Quadratic Equations

Factoring

The Quadratic Formula

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