Solve the equatio

Given: equation .

To find: Roots by completing the square method.

Method Used:

For equation: ax² + bx + c = 0, a ≠ 0

1) Make the coefficient of x unity by dividing throughout by it or if not, unity obtain .

2) Shift the constant term on RHS to get,

3) Add square of half of the coefficient of x on both sides of the equation:

4) Write LHS as the perfect square of a binomial expression and simplify RHS to get,

5) Take square on both sides to get,

6) Obtain the values of x by shifting the constant term on RHS.

Explanation:

Consider ,

To make the coefficient of x² unity divide the equation by 2,

Shift the constant term on RHS to get,

Add square of half of the coefficient of x i.e. on both sides of the equation,

As (a - b)²=a² + b² - 2ab

Now make the LHS perfect square:

⇒ x = 3 and x = 1/2

Hence the roots are 3 and 1/2.