How do you solve #x^2+6=0# by graphing?
You make the equation into one or two functions.
Starting note: I will use a standard coordination system, with y- and x-axis, this means
First look at the left side. Create the function
Next, choose some values for "x" and connect the results together with lines on a coordinate system. Alternatively, if you have access to any kind of graphing tool, use that instead.
Next, you have two options.
Either look at your graph and find the value/values for "x", where "y" is 0. This works because you know that you are looking "y" when it is 0.
Alternatively, you can define a new function from the right side of the equation. Such a function could be
Use your graphing tool to create a graph of this function too, then find where these graphs intersect, then write down the "x" value/values.
This method is more sustainable, as you might not always know exactly what "y" value to look for.
Now if you have done all that, you might have noticed something strange. The two graphs doesn't intersect! This means that there is no particular solution for
Here is the graph of
... If you must know, using complex numbers, the solution is