 Hello and welcome to the session. Let's work out the following problem. It says using quadratic formula solve the following quadratic equation for x. So, let's now start the solution. The general form of quadratic equation is given by A x square plus B x plus c is equal to 0. Now the given equation is p square x square plus p square minus q square x minus q square is equal to 0. Comparing this with the general equation we have A is equal to p square v is equal to p square minus q square and c is equal to minus q square. Now the discriminant d of the quadratic equation is given by b square minus 4ac. You must write this. Now we find d for the given equation v square that is p square minus q square whole square minus 4ac. A is p square and c is minus q square. Now we will apply the formula of A minus B whole square. So, it would be A square that is p square square plus q square square minus 2ab that is 2 into p square q square minus p square into minus q square and we know that minus into minus is plus. So, this becomes plus 4p square into q square and here we have used the formula say x minus y whole square which is equal to x square plus y square minus 2xy and this is very important to write the formulae whichever you are using. So, this is now equal to p square square is p to the power 4 q square square is q to the power 4 minus 2p square q square plus 2p square q square is equal to 2p square q square. Now this becomes the formula of p square plus q square whole square as we know that x plus y whole square is equal to x square plus y square plus 2xy and here x is p square y is q square. Now we can find the value of x, x is given by the formula minus b plus minus under the root d upon 2a. Now we substitute the values of b, d and a in the formula now v is p square minus q square plus minus under the root d that is p square plus q square whole square upon 2a is p square. So, now this is equal to minus of p square minus q square plus minus square root gets cancelled with this square. So, we have p square plus q square upon 2p square. Now we have two values of x, one is minus of p square minus q square plus p square plus q square upon 2p square and another value is x is equal to minus of p square minus q square minus p square minus q square it is plus here. So, we have plus here upon 2p square. So, we have x is equal to minus of p square plus q square since we have negative sign outside the bracket when we will open the bracket sign will change it becomes minus p square and this becomes plus q square plus p square plus q square upon 2p square and again x is minus of p square plus q square again we have negative sign outside the bracket. So, when we open the bracket sign will change. So, it becomes minus p square minus q square upon 2p square again we have now minus p square gets cancelled with plus p square and we have q square plus q square that is 2q square upon 2p square and here we have x is equal to now here plus q square gets cancelled with minus q square and we have minus p square minus p square which is minus 2p square upon 2p square now 2 gets cancelled with 2 here also and here p square gets cancelled with p square. So, we have value of x as q square by p square and x is equal to minus 1 since 2p square gets cancelled with 2p square. So, x is equal to q square by p square or minus 1. So, this completes the question while doing the question do take care of all your calculations that is very important. So, bye for now take care have a very nice day.