The equation should no remaining square roots. Use appropriate techniques to solve the equation.
Check your answer! This is not optional. When you square both sides of an equation (which has been done at least once to get this far), extraneous solutions can appear. Extraneous solutions are solutions that fit the squared equation but do not fit the original equation. Extraneous solution can appear even if no mistakes have been made! This is why the answers must be checked. Any extraneous solutions must be rejected.
Let's see this in action.
1) Isolate a square root. The square root on the right side is already by itself.
2) Square both sides:
The right side is easy to square. But the left side, with its two terms, is not as easy. We need to use FOIL or the pattern , with "a" being and "b" being 4. I like using the pattern:
which simplifies as follows:
3) We still have a square root so we repeat steps #1 and #2:
1) Isolate a square root. Subtracting x and 20 from each side we get:
Dividing both sides by 8 we get:
2) Square both sides:
which gives us:
x+4 = 0
3) The square roots are gone so we can go to step #4
4) Solve the equation. This is a very simple equation to solve. Just subtract 4 from each side:
x = -4
5) Check our solution(s), using the original equation:
Checking x = -4:
0 + 4 = 4
4 = 4 Check!
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