Question

I need help solving step by step the given equation

Answer 1

Step-by-step explanation:

The equation is given below as

`x+(6)/(x)=-7`

Multiply through by x

`\begin{gathered} x+(6)/(x)=-7 \\ x* x+x*(6)/(x)=-7* x \\ x^2+6=-7x \\ rearrange \\ x^2+7x+6=0 \end{gathered}`

By factorizing th quadratic equation, we will have

`\begin{gathered} x^(2)+7x+6=0 \\ x^2+x+6x+6=0 \\ (x^2+x)+(6x+6)=0 \\ x(x+1)+6(x+1)=0 \\ (x+6)(x+1)=0 \\ x+6=0,x+1=0 \\ x=-6,x=-1 \end{gathered}`

Hence,

The final answer is

`x=-6, x=-1`