SOLUTION: what is x^2 -4 = x we're doing 'solving equations graphically?

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Question 255656: what is x^2 -4 = x
we're doing 'solving equations graphically?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-4+=+x

Get 0 on the right by adding -x to both sides:

x%5E2-4-x=0

Let y=0

Then we can write the above as this system of equations:

system%28y=x%5E2-4-x%2Cy=0%29

Now we draw the graph of the first equation by getting
some points:

 x | y
------
-3 | 8
-2 | 2
-1 |-2
 0 |-4
 1 |-4
 2 |-2 
 3 | 2
 4 | 8



Draw a smooth curve through those points


   
Now the graph of the other equation in the system, y=0,
is simply the x-axis, so we only need to know the points where
the graph intersects the x-axis.=, and they will be the
solutions to the system

system%28y=x%5E2-4-x%2Cy=0%29

Notice that they cross at the short green lines below:



The x-intercept on the left is a little more than half way between
-1 and -2, so "guess"timate it to be -1.6.

The x-intercept on the right is a little more than half way between
2 and 3, so "guess"timate it to be 2.6.

So the solutions are about x = -1.6 and x = 2.6.

Edwin