Question

How do you solve the equation `x^2-9x=-12` by completing the square?

Answer 1

`x=9/2-sqrt33/2` or `x=9/2+sqrt33/2`

Explanation:

As we have to solve `x^2-9x=-12` by completing square method

first have alook at LHS, it appears to be of the form

`a^2-2ab+color(red)(b^2)`, where `a` is `x` tp find `b`,

letus write `-9x` as `2xx x xx (-9/2)` `-` an it is apparent that we can use `-9/2` as `b` and therefore for completing square we must add `color(red)(b^2)` i.e. `(-9/2)^2=81/4`.

Hence we can write `x^2-9x=-12` as

`x^2-9x+color(red)(81/4=-12+color(red)(81/4)`

i.e. `(x-9/2)^2=(-48+81)/4=33/4`, which can be written as

`(x-9/2)^2=(sqrt33/2)^2`

or `(x-9/2)^2-(sqrt33/2)^2=0`

Now, we can write `a^2-b^2` as `(a+b)(a-b)` and our equation becomes

`(x-9/2+sqrt33/2)(x-9/2-sqrt33/2)=0`

i.e. either `x=9/2-sqrt33/2` or `x=9/2+sqrt33/2`