 Hello and welcome to the session. In this session we will discuss the following question and the question says, solve 3 into x square minus 2 the whole is equal to 10 minus x square. Let's start the solution now. We are given the quadratic equation 3 into x square minus 2 the whole is equal to 10 minus x square. First we will open the bracket. So this implies 3 x square minus 3 into 2 which is 6 is equal to 10 minus x square. Now we will bring the terms involving the variable on one side of equality and the constant terms on the other side of equality that is we will bring minus x square on the left-hand side so the sign of minus x square would change that is we will bring minus x square on the left-hand side so the sign of minus x square would change. So this implies the left-hand side of the equality becomes 3 x square plus x square also we will bring minus 6 on the right-hand side so the sign of minus 6 would change and the right-hand side of the equality becomes 10 plus 6. This implies 4 x square is equal to 16. We now divide both the sides by the coefficient of x square. We can see that the coefficient of x square is 4. So dividing both sides by 4 we get left-hand side becomes x square and the right-hand side is 16 divided by 4 which is equal to 4. Now take the square root on both the sides so this implies x is equal to under root of 4 which implies x is equal to plus minus 2 so x is equal to 2 and x is equal to minus 2 are the two possible solutions. We will now check if these values of x satisfy the given quadratic equation. First we will check for x is equal to minus 2. Now substituting x is equal to minus 2 in the given quadratic equation we get 3 into minus 2 whole square minus 2 the whole is equal to 10 minus minus 2 whole square. Now this implies the left-hand side becomes 3 into 4 minus 2 and the right-hand side becomes 10 minus 4 which implies 3 into 2 is equal to 6. This implies 6 is equal to 6 so minus 2 satisfies the given quadratic equation. Now we check for x is equal to 2. Now substituting x is equal to 2 in the given quadratic equation we get 3 into 2 square minus 2 the whole is equal to 10 minus 2 square. This implies the left-hand side becomes 3 into 4 minus 2 and the right-hand side becomes 10 minus 4 which implies 3 into 2 is equal to 6. This implies left-hand side becomes 6 which is equal to the right-hand side which is again 6. So x is equal to 2 also satisfies the given quadratic equation. Therefore x is equal to 2 and x is equal to minus 2 is the answer for the given quadratic equation. With this we end our session. Hope you enjoyed the session.