Question

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

Answer 1

The solutions is `color(blue)(x=-3`

Explanation:

`x^2+6x+9=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*9 = 9`
AND
`N_1 +N_2 = b = 6`
After trying out a few numbers we get `N_1 = 3` and `N_2 =3`
`3*3 = 9` and `3+3= 6`

`x^2+6x+9=x^2+3x+3x+9`

`x(x+3) +3(x+3)=0`

`(x+3)(x+3)=0`

Now we equate the factors to zero and find the solutions.
`x+3 =0, color(blue)(x=-3`

`x+3 =0, color(blue)(x=-3`