SOLUTION: if the radius of a circle is increase by 4 units, its original area is multiplied by 2. Find the original radius.

Question 201095: if the radius of a circle is increase by 4 units, its original area is multiplied by 2. Find the original radius.
Found 2 solutions by Earlsdon, Alan3354:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Try this:
Original area is:

The area of the new circle is:
and , so...

Divide both sides by
Subtract from both sides.
Rewrite as a quadratic equation in standard form:
Solve using the quadratic formula: where: a = 1, b = -8, and c = -16.
Simplify:

or or approximately...
or Discard the negative solution as the radius can only be a positive value!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
if the radius of a circle is increase by 4 units, its original area is multiplied by 2. Find the original radius.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=128 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.65685424949238, -1.65685424949238. Here's your graph:

Sub r for x and ignore the negative answer.
r = 4 + 4sqrt(2)
r = ~ 9.65685

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