 Hi and welcome to the session. I am Neha and I am going to help you with the following question. The question says find the roots of the following quadratic equation if they exist by the method of completing the square. And the given equation is 2x square minus 7x plus 3 is equal to 0. Let's see its solution. We have given the equation 2x square minus 7x plus 3 is equal to 0. In this as we can see that the coefficient 2 of the term x square is not a perfect square. So to make it a perfect square we will multiply the whole equation by 2. So this will give us 4x square minus 14x plus 6 is equal to 0. Now we can write this equation as 2x whole square minus 2 into 2x into 7 upon 2 plus 6 equal to 0. Now here we have 2 into 2 that is 4x into 7 upon 2 that is 14x. Also we know that a minus b whole square is equal to a square minus 2ab plus b square. So if we compare the artist of this identity with the first two terms of the given expression then we can say that here a is 2x and b is 7 upon 2. So now to complete this whole square we just need b square. So we will add and subtract 7 upon 2 whole square to the given equation. And we will get 2x whole square minus 2 into 2x into 7 upon 2 plus 7 upon 2 whole square minus 7 upon 2 whole square plus 6 will be as it is equal to 0. Now from the first three terms we will get 2x minus 7 upon 2 whole square. Now the last two terms that is we can write them as plus minus 7 upon 2 whole square plus 6. Now let's on this one. This will be 2x minus 7 upon 2 whole square plus minus 49 upon 4 plus 6 upon 1 equal to 0. That is minus 7 upon 2 whole square plus minus 49 plus 24 upon 4 equal to 0. This gives 2x minus 7 upon 2 whole square plus minus 25 upon 4 equal to 0. This implies 2x minus 7 upon 2 whole square minus 25 upon 4 is equal to 0. Now let's transpose 25 upon 4 on the RHS. So we get minus 7 upon 2 whole square is equal to 25 upon 4. Now let's take square root on both the sides. So we'll write taking square root we get minus 7 upon 2 is equal to plus minus 5 upon 2. That means minus 7 upon 2 is equal to plus 5 upon 2 or minus 7 upon 2 is equal to minus 5 upon 2. Now we will solve both of these. So on solving the first one we will get 2x is equal to 5 upon 2 plus 7 upon 2. Which gives 2x is equal to 12 upon 2 that is 6. This implies x is equal to 6 upon 2 that is 3. Now we'll solve the second one. So this will give us 2x is equal to minus 5 upon 2 plus 7 upon 2 that is 2x is equal to minus 5 plus 7 upon 2 that is 2 upon 2 is equal to 1 is equal to 1 upon 2. So we got two values of x that is 1 upon 2 and 3. The rules of the given quadratic equation are 1 upon 2 and 3. And this is our required answer to this question. With this we've finished this session. Hope you must have understood the concept. Goodbye, take care and have a nice day.