SOLUTION: i dont no ow to do this... x-2√x=8

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Question 281500: i dont no ow to do this...
x-2√x=8
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x+-+2sqrt%28x%29+=+8
In general, to solve equations where the variable is inside a square root:
  1. Isolate a term with a square root.
  2. Square both sides of the equation.
  3. If there is still a square root, repeat steps 1 and 2 until there are no more square roots.
  4. At this point the equation should have no square roots. Use appropriate techniques to solve this equation.
  5. Check your answer(s). This is not optional. At step 2 you squared both sides of the equation. Whenever this is done, extraneous solutions may be introduced. Extraneous solutions are solutions that work in the squared equation but do not work in the original equation. So you must check your answer(s) to see if you have any extraneous solutions. Reject any extraneous solutions.

Let's see how this works on your equation.
1. Isolate a term with a square root.
You have only one such term. To isolate it (get it by itself), all we have to do is subtract x from each side:
-2sqrt%28x%29+=+8-x

2. Square both sides.
%28-2sqrt%28x%29%29%5E2+=+%288-x%29%5E2
The left side is a single term so it is easy to square. The right side is a binomial (two-term expression) so we have to use FOIL or the pattern, %28a-b%29%5E2+=+a%5E2+-2ab+%2B+b%5E2, to square it correctly:
4x+=+%288%29%5E2+-2%288%29%28x%29+%2B+%28x%29%5E2
which simplifies to:
4x+=+64+-+16x+%2B+x%5E2

3. Repeat steps 1 and 2 until there are no more square roots.
There are no square roots left so we can move to step 4.

4. Solve the equation.
This is a quadratic equation so we want one side to be zero. So we'll subtract 4x from each side:
0+=+64+-+20x+%2B+x%5E2
Then we factor (or use the Quadratic Formula). This factors easily:
0+=+%2816-x%29%284-x%29
From the Zero Product Property we know that this product is zero only if one of the factors is zero. So:
16-x = 0 or 4-x = 0
Solving these we get:
x = 16 or x = 4

5. Check your solution(s).
Always use the original equation to check:
x+-+2sqrt%28x%29+=+8
Checking x = 16:
16+-+2sqrt%2816%29+=+8
16 -2(4) = 8
16 - 8 = 8
8 = 8 Check!

Checking x = 4:
4+-+2sqrt%284%29+=+8
4 -2(2) = 8
4 - 4 = 8
0 = 8 Dose not check! We must reject this solution.

A faster, clever way to solve this is to recognize that in your original equation:
x+-+2sqrt%28x%29+=+8
you have x and sqrt%28x%29. And since x+=+%28sqrt%28x%29%29%5E2 this equation is quadratic in sqrt%28x%29. We can solve it directly as a quadratic equation:
Get one side zero:
x+-+2sqrt%28x%29+-+8+=+0
Factor:
%28sqrt%28x%29+-+4%29%28sqrt%28x%29+%2B+2%29+=+0
It can be difficult to see this factoring. If so, then try using a temporary variable:
Let q+=+sqrt%28x%29
then q%5E2+=+x
and the equation becomes:
q%5E2+-2q+-+8+=+0
The factoring should be easier to see now:
(q-4)(q+2) = 0
If we replace the q's with sqrt%28x%29 we have the factored equation we found earlier:
%28sqrt%28x%29+-+4%29%28sqrt%28x%29+%2B+2%29+=+0
Use the Zero Product Property:
sqrt%28x%29+-+4+=+0 or sqrt%28x%29+%2B+2+=+0
Solving:
sqrt%28x%29+=+4 or sqrt%28x%29+=+-2
Since square roots cannot be negative, we reject the second equation. Solving the first equation we square both sides:
x = 16
Check the solution. (We checked this above and it works.)