Question

How do you use factoring to solve this equation `x^2+x=56`?

Answer 1

`x^2+x=56`
`x^2+x - 56 = 0`

We can Split the Middle Term of this expression to factorise it.

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*(-56) = -56`
and
`N_1 +N_2 = b = 1`

After trying out a few numbers we get `N_1 = 8` and `N_2 =-7`
`8*(-7) = -56`, and `8+(-7)= 1`

`x^2+x - 56 = x^2+8x - 7x - 56`
`x(x +8) - 7(x+8)`

`(x-7)(x +8)` is the factorised form

`color (red)(x = 7, x = -8` are the solutions for the expression.