Solve each equation using the quadratic formula. See Examples 5 a...

Question

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - x - 1 = 0

Accepted Answer

Hello, everyone. We're going to use the quadratic formula to find the value of X in the equation two X squared minus 74 X plus equals zero. So I recall that I need to have my equation set up as A X squared plus BX plus C equals zero in order to use the quadratic formula. And in this case, it is set up that way already for us. So I'm going to define what A B and C are A is to B is -74 and C is 673. Now, that number looks a little intimidating but it'll work out next. I'm gonna write out what the full quadratic formula is just so I can reference it if I need to X equals negative B plus or minus the square root of B squared minus four A C all over two A. So now that I have all that down, I'm gonna plug it in for my A B and C. So X equals negative B which is the opposite of B so plus or minus the square root of negative squared minus four. Times A which is two times C which is 673 all over two A so two times two. So next, I'm going to multiply what's under my radical. So I still have 74 plus or minus the square root. And now I need to do negative 74 squared and that's 5476 And then -4 times two times 673. And that comes out to Over two times 2, which is four. So x equals and then I'm going to subtract the numbers under my radical. So 74 plus or minus the square root of when I subtract those I get 92, that number is not as bad as I had feared. It could have been over four. So now I know I need to simplify the square root of 92. I'm gonna do it off to the side and then plug it back into the formula. So I'm looking for a perfect square that goes evenly into 92. My gut says the square to four times the square to 23 is my best, but square to four is two. So the square to 92 is the same as the two times the square of 23. So I'm gonna put that back into my quadratic formula that I was working on X equals 74 plus or -2 times the square to 23. Over four. Looking at what I have so far, I recognize that each term is divisible by two. So I'm gonna divide them all by two And I get x equals so half of 74 is 37 plus or minus The squared of 23 because those twos would cancel. And then four, sorry, four, reduced by two is two. So my X values are 37 minus the square root of 23/2 And plus the square root of 23/2. Those are my two solutions. And when I look that is answer choice. D have a nice day.

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Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - x - 1 = 0

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