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

1 Answer
Oct 11, 2015

Answer:

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#