Question

How do you solve `x^2-2x=8`?

Answer 1

`color(blue)(x=-2`
`color(blue)(x=4`

Explanation:

`x^2−2x- 8 = 0`

We can Split the Middle Term of this expression to factorise it and thereby find the solutions:

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*-8 = -8`
AND
`N_1 +N_2 = b = -2`

After trying out a few numbers we get `N_1 = -4` and `N_2 =2`
`2*(-4) = -8` and `2 + (-4)= -2`

`x^2−2x- 8 = x^2 color(blue)(- 4x + 2x)- 8`

`= x( x-4) + 2(x - 4)`

`color(blue)((x+2) ( x-4)` is the factorised form for the expression, we now equate the factors to zero and obtain the solutions.

`x+2 = 0, color(blue)(x=-2`
`x-4 = 0, color(blue)(x=4`