TenMarks teaches you how to solve quadratic equations using the quadratic formula.
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Learn about the Quadratic Formula Solve quadratic equation using the quadratic formula. So in this problem we need to solve using the quadratic formula. So before we begin, the solutions of ax2+bx+c=0 where A is not equal to zero so remember is not equal to zero. So the solutions are x=-b+-v(b2-4ac)/2a. And this is known as the quadratic formula. so let’s use this and go ahead and solve our formula or solve our equations using this quadratic formula. So here, we have first problem 4x2-4x-3=0 so the steps, the first step we need to is make sure it’s written in standard form and standard form is written such as this so this is standard form, ax2+bx+c=0 so that’s standard form. So to write it, it would be 4x2+-4x+-3=0. So now this is in the standard form. So our second step is we need to identify a, b and c so in this formula a—in standard form it’s ax2 so A would be four, b would be negative four, and c would be negative three. Now, we’re going to use the quadratic formula. I’m going to give myself some more room for the next problem. So now, we’re going to use the quadratic form and remember our quadratic formula I’m just going to rewrite it here for us so it’s x=-b+-vb2-4ac/2a. So now, we’re going to make our substitutions. So X=-b, negative b is four, so be negative four plus or minus the square root of negative four squared minus four times A which is four times C which is negative three and then over two times A which is four. Now, we’re going to go ahead and simplify. So our next step then is to simplify. So to simplify, I’m going to take X equals negative four times negative one times negative four be four plus or minus the square root of well negative four squared is a positive 16 and then negative four times four times negative three would be a positive 48 over two times four which is eight. So now I have—and then simplify even more so now I have x=4+-v(16+48) is 64/8. And then the square root of 64 is 4+-8/8 and give myself some more room again keeping it out. So now, we’re ready for our step five which is to write as to equations. So here, we’re going to have our first equation so it’s x=4+-8/8 so our first equation will be x-4+8/8 and then our second equation would be x=-8/8. So now, our sixth step is to solve so x=4+8/8 would mean that 4+8 is 12/8 which would be 3/2 or x=4-8/8 and then 4-8 is -4/8 which would be -1/2. So the solutions to these problems are x=3/2 or x=-1/2. Let’s go ahead and move on to our next problem here. So the first step in solving 2x=-4+2x2 is we need to write in standard form. Remember what standard form is? Standard form is ax2+bx+c=0. So to put 2x=-4+2x2 in standard form what we’re going to do first is we have to move this over, so we’re going to have—we’re going to move the 2x over. So we’re going to have 2x2+—because were moving the negative—or the 2x over here so we plus a -2x+-4 and that equals zero so now, we’re in standard form. Now, our second step is we need to identify a, b and c so a would equal two, b would in this formula that middle one so b is negative two and c is negative four. So now, we’re going to use our quadratic equation so the quadratic equation remember is x=-b+-vb2-4ac/2a so we’re going to go ahead and make our substitutions. So x equals b is two is b negative or minus negative two plus or minus square root of b which is negative two so I’m going to take negative two squared minus four times a which is two times c which is negative four over two times a which is two. So I’m going to go ahead and simplify this so our next step is to simplify so that be x equals negative two—negative times negative two would be two plus or minus square root of negative two square could be four plus four times two is eight, negative four times two is eight times negative four which would be 32 and then two times two is four and that would give us x=2+-v36/4. So the square root of 36 is x=2+-6 so square root of 36 is 6/4. So now, we’re going to write these two—this is two equations so o