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 - 3x - 2 = 0

Accepted Answer

Hello, everyone. We're going to use the quadratic formula to find the value of X in the equation three X squared minus 14 X plus 10 equals zero. First thing I recall is that to use the quadratic formula, I want my equation to be set up as A X squared plus BX plus C equals zero. Looking at the equation we were given it is in that format. So I'm going to define my A B and C A is three, B is negative 14 C is 10. And then just so I have it for reference, I'm going to write out the quadratic formula over here. So X equals negative B plus or minus the square root of B squared minus four A C over two A. Now that I have all of that written out, I'm gonna plug my values in. So X equals negative B or the opposite of B so plus or minus the square root of negative 14 squared -4 times a which is three times c which is 10 all over two times A. So two times three, Next, I'm going to multiply what I can under my radical. So x equals 14 plus or minus. And then the square root um negative 14 squared is 196 And then -4 times three times 10 is 120 Over two times 3, which is six. So I'm going to combine the numbers under my radical. So X equals 14 plus or minus the square root of 76/6. I know I need to reduce the square root of 76. I'm gonna do it off to the side. So that way if I make a little mistake, I have a spot where I can fix it. I know we want to factor a perfect square out of there. The first one that comes to my mind is four. So I'm going to check that. So it looks like the square to four times the square root of 19 would give me the square root of 76 square root of four is the same as two. So too radical 19 is the same as the square root of 76. And I'm gonna plug that in to my quadratic formula. So I now have 14 plus or -2 square to 19/6. Next, I want to reduce if I can, I notice that all the terms that I have left are divisible by two. So I'm gonna divide them all by two. So I have seven plus or minus the square root of over three. And in the interest of writing this is a full solution set. I'm going to write that as two separate answers. So I get seven minus the square root of 19/3 and X also equals seven plus the square root of 19/3. Those are my two solutions and looking at my answer choices that would be answer choice C have a nice day.

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Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - 3x - 2 = 0