Question

The equation 3x^2-6x=8 is rewritten in a form of 3(x-p)^2+q=0.

Answer 1

`3(x - 1)^2 - 11= 0`

Explanation:

Given

`3x^2 - 6x = 8`

Required

Rewrite in form of
`3(x - p)^2 + q = 0`

`3x^2 - 6x = 8`

Subtract 8 from both sides

`3x^2 - 6x - 8 = 8 - 8`

`3x^2 - 6x - 8 = 0`

Express -8 as 3 - 11;

So, we have:

`3x^2 - 6x + 3 - 11= 0`

Expand
`3x^2 - 6x + 3`

`3(x^2 - 2x + 1) - 11= 0`

Factorize the expression in the bracket;

`3(x^2 - x -x + 1) - 11= 0`

`3(x(x - 1) -1(x - 1)) - 11= 0`

`3((x - 1)^2) - 11= 0`

`3(x - 1)^2 - 11= 0`

By comparison:
`3(x - p)^2 + q = 0`

`p= 1`

`q = -11`