SOLUTION: Solve algebraically and check your potential solutions: squareroot of x+20-x=0

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Question 164117This question is from textbook
: Solve algebraically and check your potential solutions: squareroot of x+20-x=0 This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x, check solutions:
sqrt%28x%2B20%29-x+=+0 Is this right? You really ought to use parentheses around the radicand to make it clear.
sqrt%28x%2B20%29-x+=+0 Add x to both sides.
sqrt%28x%2B20%29+=+x Square both sides.
x%2B20+=+x%5E2 Rewrite this as:
x%5E2-x-20+=+0 Factor.
%28x%2B4%29%28x-5%29+=+0
x%2B4+=+0 or x-5+=+0, so...
x+=+-4 or x+=+5
Check:
sqrt%28x%2B20%29-x+=+0 Substitute x = -4.
sqrt%28-4%2B20%29-%28-4%29+=+sqrt%2816%29%2B4 Evaluate.
sqrt%2816%29%2B4++=+4%2B4= 8 Nope! or sqrt%2816%29%2B4+=+-4%2B4 = 0 OK!
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sqrt%28x%2B20%29-x+=+0 Substitute x = 5.
sqrt%285%2B20%29-5+=+sqrt%2825%29-5 Evaluate.
sqrt%2825%29-5+=+5-5=0 OK! or -5-5+=+-10 Nope!