Question

How do you solve `x+4=-4/x`?

Answer 1

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

Explanation:

`x+4=-4/color(blue)(x`

`color(blue)(x) * (x+4)=-4`

`x^2 +4x =-4`

`x^2 +4x +4=0`

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

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`

`x(x+2) +2(x +2)=0`

`(x+2)(x+2) =0`

We now equate the factor to zero to obtain the solution(both factors are equal here):

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