SOLUTION: solve the eqaution. If the equation has no real solution, so state. square root of q + 4 = 5

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Question 245459: solve the eqaution. If the equation has no real solution, so state.
square root of q + 4 = 5
Found 2 solutions by Earlsdon, jsmallt9:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for q:
sqrt%28q%2B4%29+=+5 Square both sides.
q%2B4+=+25 Subtract 4 from both sides.
highlight%28q+=+21%29

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28q%2B4%29+=+5 or sqrt%28q%29+%2B+4+=+5? (Use parentheses to make things clear, please.) I'll do both.

Solving equations like these involve:
  1. Isolate a square root on one side of the equation.
  2. Square both sides.
  3. If there are still square roots, repeast steps #1 and #2 until they are gone.
  4. Solve the equation once the square roots are gone.
  5. Check your answers!! This is more than just a good idea. It is important because at step #2 you squared both sides of an equation. And squaring both sides of an equation can interodcue what are called extraneious solutions. These are solutions which fit the squared equation but do not fit the original equation! So we have to check all solutions, in the original equation to make sure they actually work.

sqrt%28q%2B4%29+=+5
The square root is already all by itself on the left side so we can proceed to squaring both sides:
%28sqrt%28q%2B4%29%29%5E2+=+%285%29%5E2
q%2B4+=+25
The square root is gone so we solve this. Subtract 4 from eqch side:
q+=+21
Checking q = 21:
sqrt%28q%2B4%29+=+5
sqrt%2821%2B4%29+=+5
sqrt%2825%29+=+5
5+=+5 Check!

sqrt%28q%29+%2B+4+=+5
Isolate the square root. Subtract 4 from each side:
sqrt%28q%29+=+1
Square both sides:
%28sqrt%28q%29%29%5E2+=+%281%29%5E2
q+=+1
This equation is already solved so we can proceed to checking the answer:
sqrt%28q%29+%2B+4+=+5
sqrt%281%29+%2B+4+=+5
1+%2B+4+=+5
5+=+5 Check!

Note: Both answers checked out. But this doesn't mean that it was a waste of time to check them. There will be problems like these where one or more (maybe all) "solutions" do not actually work in the orginal equation so we cannot forget to check the answers any time you square both sides of an equation!