Solve the quadratic equation `x^(2) - 12x + 32 = 0 ` by completing square method`:`

Answer

4,8 are the roots of the given quadratic equation.

Explanation

Comparing `x^(2) - 12x ` wih `x^(2) +2xy`
`2xy = -12 x " " :. 2y = - 12 " " y = -6` ` :. y ^(2) = 36`
`x^(2) - 12x + 36` is a perfect square trinomial .
`x^(2) - 12x + 32 = 0`
`:. X^(2) - 12x + 36 - 36 + 32 = 0`
`(x-6)^(2) - 4= 0 `
`:. (x-6)^(2) - ( 2)^(2) = 0 `
` :. ( x- 6+2) ( x- 6-2) = 0 `
`:. ( x- 4) ( x- 8 ) = 0 `
`:. x - 4 = 0 ` or ` x- 8 = 0 `
` :. x = 4 ` or ` x= 8 `