Question

How do you solve `x^2+6x+2=9` by factoring?

Answer 1

The solutions are:

`color(blue)(x=1`
`color(blue)(x=-7`

Explanation:

`x^2+6x+2=9`
`x^2+6x+2-9=0`
`x^2+6x-7=0`

We can Split the Middle Term of this expression to factorise it and then we 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*-7 = -7`
and
`N_1 +N_2 = b = 6`

After trying out a few numbers we get `N_1 = 7` and `N_2 =-1`
`7*(-1) = -7`, and `7+(-1)= 6`

`x^2+6x-7 = x^2+7x-1x-7`
`x(x+7)(-1(x+7)=0`
`(x-1)(x+7)=0`
Now we equate the factors to zero and find the solutions.

`x-1=0,color(blue)(x=1`
`x+7=0,color(blue)(x=-7`