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

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Answer 1 · 2015-10-11T12:17:29

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

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

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

$x^2 +4x =-4$

$x^2 +4x +4=0$

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):

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

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