Solve each equation. 2x²+x-15 = 0

Question

Accepted Answer

Hello, today we're going to be solving the following quadratic equation. So what we are given is three X squared plus X minus 56 is equal to zero. And we're going to solve this using the quadratic equation. And the quadratic equation states that X is 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 given equation. So in the equation, the coefficient of the first term is going to be three. So A is going to equal to three, the coefficient of the second term is 17. So B is equal to 17 and the last term is going to be negative 56. So we're going to let C equal to negative 56. So if we take these three values and plug it into the quadratic equation, what we have is X is equal to negative B which is negative 17 plus or minus the square root of B squared which is 17 squared minus four times A which is three times C which is negative 56 all divided by two times A which is two times three. Now let's go ahead and simplify 17 squared is going to give us 289 And -4 times three times negative 56 is going to give us 672. So what we have is X is equal to negative 17 plus or minus the square root of 289 plus 672 All divided by two times 3, which is going to give us six. Now, 289 plus 672 is going to give us 961. So we have X is equal to negative 17 plus or minus the square root of 961 divided by six. And the square root of 961 is going to simplify to give us 31. So what we have is X is equal to negative 17 plus or -31 divided by six. And now, since this is a plus or minus statement, we're going to separate this into two equations. We have one equation where X is equal to negative 17 plus divided by six. And we have the other equation where X is equal to negative 17 minus 31 divided by six. And we're gonna go ahead and solve both of these equations. Now, on the left hand side, negative 17 plus 31 is going to give us 14. So X is equal to 14/6. Now we can divide the numerator and denominator by two and that is going to give us X is equal to 7/3, which is going to be the first solution for X. Now, on the right hand side, negative 17 minus 31 is going to give us negative 48. So we have X is equal to negative 48 divided by six and negative 48 divided by six is going to give us negative eight. So X is equal to negative eight. And so what this means is that there's gonna be two solutions for X X is equal to 7/3 and X is equal to negative eight. And 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+x-15 = 0

Key Concepts

Quadratic Equations

Factoring

The Quadratic Formula

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