Question

How do you solve `x^2=12x-27`?

Answer 1

`x^2=12x-27`
`x^2 -12x+27=0`

We can Split the Middle Term of this expression to factorise it and thereby find the solution.
In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 1*27 = 27`
And
N_1 +N_2 = b = -12#

After trying out a few numbers we get `N_1 = -9` and `N_2 =-3`
`9*3 = 27`, and `-9+(-3)= -12`

`x^2 -12x+27= x^2 -9x - 3x +27`
`x(x - 9) - 3(x-9) = 0`

`color(green)((x-9)(x - 3)` is the factorised form.
and `color(green)(x=9 and x=3` are the solutions.