SOLUTION: Find all real or imaginary solutions to the eqyation. sqrt[7x+29]=x+3

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Question 122489: Find all real or imaginary solutions to the eqyation.
sqrt[7x+29]=x+3

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%287x%2B29%29+=x%2B3...rise boyh sides to the 2 power
%28sqrt%287x%2B29%29%29%5E2=+%28x%2B3%29%5E2...
7x%2B29=+%28x%2B3%29%5E2...
7x%2B29=+x%5E2+%2B+6x+%2B+9...
0+=+x%5E2+%2B+6x+-7x+-+29+%2B+9...
+x%5E2+-+x+-+20+=+0......use quadratis formula
x%5B1%2C2%5D+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+


x%5B1%2C2%5D+=+%281+%2B-+sqrt%28+1+%2B+80+%29%29%2F2+
x%5B1%2C2%5D+=+%281+%2B-+sqrt%28++81+%29%29%2F2+
x%5B1%2C2%5D+=+%281+%2B-+%28++9%29%29%2F2+

x%5B1%5D+=+%281+%2B+%28++9%29%29%2F2+
x%5B1%5D+=+10%2F2+
x%5B1%5D+=+5

x%5B2%5D+=+%281+-+%28++9%29%29%2F2+
x%5B2%5D+=++-%288%29%2F2+
x%5B2%5D+=+-+4

check:
sqrt%287x+%2B+29%29+=x%2B3...plug in x%5B1%5D+=+5
sqrt%287%285%29%2B29%29+=+5%2B3...
sqrt%2835+%2B+29%29+=+8...
sqrt%2864%29+=+8...
8+=+8...

sqrt%287x+%2B+29%29+=x%2B3...plug in x%5B1%5D+=+-4
sqrt%287%28-4%29%2B29%29+=+-4%2B3...
sqrt%28-28+%2B+29%29+=+-1...
sqrt%281%29+=+-1................since sqrt%281%29=%28%2B1_or_-1%29, we can write
-1=+-1...