COMPLETING SQUARE | SOLVE QUADRATIC EQUATIONS BY COMPLETING SQUARE | 10TH CLASS MATHEMATICS

SOLUTION OF QUADRATIC EQUATIONS BY COMPLETING SQUARE METHOD EXPLAINED IN URDU/HINDI 10TH CLASS MATHEMATICS

SOLUTION OF QUADRATIC EQUATIONS BY COMPLETING SQUARE:

·         In this method here are a few steps to follow:

i)                    First of all make the coefficient of x² ‘1’.

ii)                  Take the constant ‘c’ to the right hand side of the quadratic equation.

iii)                Now multiply the coefficient of ‘x’ by ‘1/2’ and then square.

iv)                Add that squared term to the both sides of the equation.

v)                  Simplify the equation as much as possible.

vi)                Take square root of the both sides of equation.

vii)              Simplify to possible extent and find values of variable.

viii)            Write solution set.

Example:-        Solve the equation by completing square method.

                        x² – 3x – 4 = 0

Firstly, we have to make coefficient of x² ‘1’ which is already ‘1’.

Now, take the constant term to the right hand side of the equation.

                        x² – 3x = 4

In this step, we are to multiply coefficient of ‘x’ b by ‘1/2’.

As we know     a = 1, b = -3, c = -4

So,       b x 1/2 = -3 x 1/2 = -3/2 

Squaring,         (-3/2)²  and then adding (-3/2)² to the both sides of the equation.

                        

                          x²  - 3x + (-3/2)²  = 4 + (-3/2)²

Here we see that on the L.H.S of the equation, a complete square is being formed .

As we know (a – b)² = a² – 2ab + b² , so by this formula, we see the above equation forming a complete square on the left side.

Therefore,        (x – 3/2)²          =          4 + 9/4

                      

                          (x – 3/2)²          =          16 + 9 /4

                        √

                          (x – 3/2)²       =          ± √25/4

                        

                         (x – 3/2)           =          ±5/2

or                                 x          =          3/2 ± 5/2

Here two possibilities may arise, we take either +5/2 or -5/2

So,       x = 3/2 + 5/2                            or                     x = 3/2 – 5/2

x = 8/2 & x = 4                                                or                     x = -2/2 & x = -1\

Therefore, solution set is {-1, 4}

                                                           

For understanding more comprehensively, watch the video from start to end and full procedure of solving the Quadratic Equations by completing square has been explained with many examples.

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