SOLUTION: (P+8)^2=13

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Question 232506: (P+8)^2=13
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28P%2B8%29%5E2=13
The quick way to solve this is to find the square root of each side:
sqrt%28%28P%2B8%29%5E2%29=sqrt%2813%29
abs%28p%2B8%29+=+sqrt%2813%29
p%2B8+=+sqrt%2813%29 or p%2B8+=+-sqrt%2813%29
Solving these we get:
p+=+-8+%2B+sqrt%2813%29 or p+=+-8+-+sqrt%2813%29
Although this way was fast, it was tricky. One has to know that sqrt%28x%5E2%29+=+abs%28x%29, not x. And then one has to know how to handle the absolute value equation correctly.

A longer but perhaps less tricky way would be to multiply out the left side:
p%5E2+%2B16x+%2B64+=+13
Subtract 13 from each side:
p%5E2+%2B16x+%2B51+=+0
Then factor or use the quadratic formula. This will not factor so we have to use the quadratic formula. And when we use it correctly we end up with the answers we found the short but tricky way.