 okay friends so we have again taken our quadratic equation and we have to solve this using completing the square method so we studied completing the square method in the previous session if you have not checked it so I would request you you can go back to the previous video link and see that and then come and solve this equation again so how to do it so we will go step by step so first step is divide the entire equation by the coefficient of x square so hence dividing dividing let's say we name it equation 1 dividing 1 by 4 so coefficient of x square what will it be it will be x square plus bx minus a square minus b square upon 4 equals 0 next step second step is keep the variables on one side and the constant term on the other side so hence I will write a square minus b square y4 so I took a square minus b square upon 4 on to the right-hand side okay now what add what do we add here we add x square plus so and you know you can write bx this bx as 2 times x times b upon 2 right so this is a this is a you know a critical step for completing the square method so I'm writing bx as 2 times x separate x first y because x is linked to this x square and then b by 2 this will give us an indication of to how to complete the square so fourth term fourth step you can write x square plus 2 times x times b by 2 plus b by 2 whole square so I'm adding this square term right but if I'm adding this I have to add on the right-hand side as well so b by 2 whole square and then plus a square minus b square by 4 is it this is what the equation would look like and why did I add b by 2 on the left-hand side and where did I get this b by 2 I got the indication from here so if you see the left-hand side is now the square term of x plus b by 2 whole square right and this is equal to if you now you know solve the right-hand side so b square plus 4 plus a square minus b square by 4 okay which can be further simplified as the denominator is common here isn't it so b square plus a square minus b square so b square b square goes a square by 4 so this implies x plus b by 2 whole square is equal to a square by 4 correct now what you can do is either you write this as x plus b by 2 you're squaring square rooting both sides you will get plus minus a by 2 right if you take the square root both sides what does it mean this means I did this step x plus b by 2 whole square take the square root of this is equal to under root a square by 4 but this is you know this is not right way to do it because under square root of anything is always positive it's never a negative term so hence the best way I would prefer this method so what I do normally is I write x plus b by 2 square minus a by 2 whole square if you see a square by 4 is a by 2 whole square and this is equal to 0 now this is reduced to difference of square term so hence now what you can do you know factorize it like this x plus b by 2 consider it to be a and then minus a by 2 yeah so this is nothing but it indicates a square minus b square form so this is nothing but a minus b times a plus b so that's what I am doing in the LHS okay so hence what is this equation is then reduced to x plus b by 2 plus a by 2 and this is equal to 0 correct so now we have time and again done this or you know simplify again to get a better look so let us say we say x plus b minus a by 2 this is one factor another factor is x is plus a plus b by 2 if you rearrange and see it will be like that correct so hence what so I can equate this term this factor to be 0 and this factor to be equal to 0 and you will get the result so hence you will get either x plus b minus a by 2 is 0 or x plus a plus b by 2 is equal to 0 so this implies x is equal to minus b minus a by 2 or x is equal to minus a plus b upon 2 right which is also equal to this x can be written as a minus b by 2 or this x can be written as minus a minus b whole upon 2 okay so these are the two solutions of the given quadratic equation so we used what completing the square method to solve this equation the equation was 4 x square plus b x 4 x square plus 4 b x minus a square minus b square equals to 0