Question

How do you solve `7r^2 - 14r= -7` by factoring?

Answer 1

The solution is `color(blue)(r=1`

Explanation:

`7r^2-14r=-7`

`7r^2-14r+7=0`

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

In this technique, if we have to factorise an expression like `ar^2 + br + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 7*7 =49`
and
`N_1 +N_2 = b = -14`

After trying out a few numbers we get `N_1 = -7` and `N_2 =-7`
`-7*-7 = 49`, and `(-7)+(-7)= -14`

`7r^2-14r+7=7r^2-7r-7r+7`
`7r^2-7r-7r+7=0`

`7r(r-1) -7(r-1)=0`

`color(blue)((7r-7)(r-1)=0`

We now equate these factors to zero

`7r-7=0, color(blue)(r=1`
`r-1=0, color(blue)(r=1`