Question

Please solve equation for x with steps 1/3x= 1/3+ 6/x

Answer 1

The given equation is

`(1)/(3)x=(1)/(3)+(6)/(x)`

First, we subtract 6/x on each side

`(1)/(3)x-(6)/(x)=(1)/(3)+(6)/(x)-(6)/(x)\rightarrow(1)/(3)x-(6)/(x)=(1)/(3)`

Second, we solve the difference in the left side of the equation

`(x^2-18)/(3x)=(1)/(3)`

Third, we simplify numbers 3, and multiply the equation by x

`(x(x^2-18))/(x)=x\rightarrow x^2-18=x`

Fourth, we subtract x on each side to get the quadratic equation

`x^2-18-x=x-x\rightarrow x^2-18-x=0`

Additionally, we need to find two number which product is 18, and which difference is 1. Those numbers are no integers, so, we must use a calculator.

Using a calculator, the solutions are

`x_1=4.77,x_2=-3.77`