Question

How do you solve `5x^2-30x+5=0` by completing the square?

Answer 1

`x=3-2sqrt2` or `x=3+2sqrt2`

Explanation:

To solve `5x^2-30x+5=0`, let us first divide both sides by `5` whic gives us

`x^2-6x+1=0`

Now to complete square for `x^2-6x`, recalling identity `(x-a)^2=x^2-2ax+a^2`, we must add and subtract square of half of the coefficient of `x` i.e. `(6/2)^2=9`, hence we have

`x^2-6x+9-9+1=0` or

`(x-3)^2-8=0` or `(x-3)^2-(2sqrt2)^2=0` which can be factorized as

`(x-3+2sqrt2)(x-3-2sqrt2)=0`

Hence `x=3-2sqrt2` or `x=3+2sqrt2`