Solve each equation. x²- √5x -1 = 0

Question

Accepted Answer

Hello, today we're going to be solving the quadratic equation. So what we are given is X squared minus the square root of six, X minus one is equal to zero. Now, in order to solve this equation, we're going to use 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 try no meal. So here a is going to be the coefficient of the first term which in this case is going to be one B is going to be the coefficient of the second term which is going to be the negative square root of six and C is going to be the constant, which is going to be negative one. So if we take these values of A B and C and plug them into the quadratic equation, what we have is X is equal to negative B which is going to be negative negative square root of six, which is going to give us positive square root of six plus or minus the square root of negative square root of six squared minus four times A which is one times C which is negative one all over two times A which is two times one. And now we just need to go ahead and simplify in the numerator, negative square root of six squared is the same thing as saying the negative square root of six times the negative square root of six and a negative number times a negative number is going to produce a positive number. And the product of two square roots can be combined into a single square root. So we can simplify this to be the positive square root of six times six, Which is going to give us the square root of 36, which simplifies to positive six. So in the numerator, we have the square root of six plus or minus the square root of six and we have negative four times one times negative one, which is going to give us positive four. So six plus four all over two times one, which is going to be two. Now 6-plus 4 is going to give us 10. So we have X is equal to the square root of six plus or minus the square root of 10, all divided by two. And at this point, since we have a plus or minus statement, we can go ahead and split this up into two equations. So we have X is equal to the square root of six plus the square root of all divided by two and X is equal to the square root of six minus the square root of 10, all divided by two. And this is going to be the two solutions to the giving quadratic equation. And with that being said, the answer to this problem is going to be D. 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.

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Solve each equation. x²- √5x -1 = 0

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