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

Oct 11, 2015

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

#### Explanation:

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

$\textcolor{b l u e}{x} \cdot \left(x + 4\right) = - 4$

${x}^{2} + 4 x = - 4$

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

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 $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 4 = 4$
AND
${N}_{1} + {N}_{2} = b = 4$

After trying out a few numbers we get ${N}_{1} = 2$ and ${N}_{2} = 2$
$2 \cdot 2 = 4$, and $2 + 2 = 4$

${x}^{2} + \textcolor{b l u e}{4 x} + 4 = {x}^{2} + \textcolor{b l u e}{2 x + 2 x} + 4$

$x \left(x + 2\right) + 2 \left(x + 2\right) = 0$

$\left(x + 2\right) \left(x + 2\right) = 0$

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

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