First draw a graph to see the likely value.
Looks like it might be x = -2.
Try x=2
-2+6 = 4
0.5-2 = 1/2-2 = 22 = 4
So x = 2.
If you prefer a numerical approach rewrite the equation as 2x = 1/(x+6)
Take log2 of both sides
x = log2(1/(x+6)) ...(1)
Make an initial guess for x, say x = -1. Plug this into the right-hand side of equation (1) to get a new estimate for x. Plug this new value into the right-hand side of equation (1) to get yet another estimate, and so on. Repeat until you converge on a unique value. In this case the process will converge on the number -2 in 9 or 10 iterations.
First draw a graph to see the likely value.
Looks like it might be x = -2.
Try x=2
-2+6 = 4
0.5-2 = 1/2-2 = 22 = 4
So x = 2.
If you prefer a numerical approach rewrite the equation as 2x = 1/(x+6)
Take log2 of both sides
x = log2(1/(x+6)) ...(1)
Make an initial guess for x, say x = -1. Plug this into the right-hand side of equation (1) to get a new estimate for x. Plug this new value into the right-hand side of equation (1) to get yet another estimate, and so on. Repeat until you converge on a unique value. In this case the process will converge on the number -2 in 9 or 10 iterations.