Question

How do you solve `x^2+4x+4=0` by factoring?

Answer 1

The solution is
`color(blue)(x=-2`

Explanation:

`x^2+4x+4=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*4 = 4`
AND
`N_1 +N_2 = b = 4`

After trying out a few numbers we get `N_1 = 2` and `N_2 =2`
`2*2 = 4`, and `2+2= 4`

`x^2+color(blue)(4x)+4= x^2+color(blue)(2x +2x)+4=0`

`=x(x+2 ) +2(x+2)`

`color(blue)((x+2)(x+2 )` are the factors of the expression.

Now we equate these factors to zero to find the solutions.

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