Question 916327: The distance d, to the horizon of an object h miles above a planet's surface is given by the equation {d= sqrt(6319h+h^2)}. How many miles above the planets surface is a satellite if the distance to the horizon is 720 mi?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! All that is expected is that you plug the value for the distance to the horizon  into the equation  ,
and then solve for  .
 .
The solutions to that equation will also be solutions to the equation we get by squaring both sides of the equal sign.
(The new equation may have some other extra solutions, but we will worry about that later).
Squaring both sides of the equal sign, we get
 ---> --->
That quadratic equation can be solved by factoring,
if you realize that  and  .
Then you would know that
 ,
and you would look for the solutions to the equivalent equation
 , which are  and  .
So, the satellite is  miles above the planet's surface.
Of course, is an extraneous solution,
meaning that is not a solution of the original equation,
but it is a solution we "gained" when we squared both sides of the equal sign.
If you do not solve by factoring, you can always get the same results by applying the quadratic formula (or by completing he square).
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