Question

Solve the following quadratic equations by factorization:

`(x-1/2)^2=4`

Answer 1

We have,

`(x-1/2)^2=4`

`(x-1/2)^2-4=0`

`(x-1/2)^2-(2)^2=0`

`rArr[(x-1/2)+2][(x-1/2)-2]=0`          ......[∵ a² - b² = (a + b)(a - b)]

`rArr(x-1/2+2)=0` or `(x-1/x-2)=0`

`rArrx=2-1/2` or `x=2-1/2`

`rArrx=(4-1)/2` or `x=(4+1)/2`

`rArrx=3/2` or `x=5/2`

Hence, `x=3/2` or `x=5/2`