 Hello and welcome to the session. The given question says solve for x and the given quadratic equation is 4x square minus 2 times of a square plus b square into x plus a square into b square is equal to 0. Let's start with the solution. So let us write down the given equation where just 4x square minus 2 times of a square plus b square into x plus a square into b square is equal to 0. Or it can further be written as 4x square minus on opening the brackets we have 2 a square into x minus 2 times of b square into x plus a square into b square is equal to 0. Now we shall take the common factors from the first 2 terms and the last 2 terms. Thus it can further be written as taking 2x common from the first 2 terms we have 2x minus a square. Now taking minus b square common from the last 2 terms we have 2 times of x minus a square is equal to 0. Now taking 2x minus a square common it can further be written as 2x minus a square into 2x minus b square is equal to 0. Now as we know if the product of 2 numbers is equal to 0 so this implies either a is 0 or b is 0 so from here we can say that either minus a square is equal to 0 or 2x minus b square is equal to 0. Now to get the value of x let us source both these equations one by one starting with the first one which is 2x minus a square is equal to 0. So this implies that x is equal to a square divided by 2 and the second equation is 2x minus b square is equal to 0 and on solving we have x is equal to b square divided by 2. Hence our answer is on solving the given equations for x our answer is a square divided by 2 and b square divided by 2. So these two are the values of x this completes the session hope you understood it well bye and take care.