Question

Solve the following quadratic equation by factorization:

`(x-5)(x-6)=25/(24)^2`

Answer 1

We have been given that,

`(x-5)(x-6)=25/(24)^2`

`(x-5)(x-6)=25/576`

`x^2-11x+30-25/576=0`

`x^2-11x+17255/576=0`

`x^2-145/24x-119/24x+17255/576=0`

`x(x-145/24)-119/24(x-145/24)=0`

`(x-119/24)(x-145/24)=0`

Therefore,

`x-119/24=0`

`x=119/24`

or,

`x-145/24=0`

`x=145/24`

Hence, `x = 119/24 = 4 23/24` or `x = 145/24 = 6 1/24`