SOLUTION: Find all real or imaginary solution to the equation. {{{sqrt(7x+29)=x+3}}}

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Question 42227: Find all real or imaginary solution to the equation.
sqrt%287x%2B29%29=x%2B3
Found 2 solutions by fractalier, psbhowmick:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Okay from
sqrt(7x + 29) = x + 3
we square both sides and get
7x + 29 = (x + 3)^2
7x + 29 = x^2 + 6x + 9
now collect terms and rearrange
x^2 - x - 20 = 0
(x - 5)(x + 4) = 0
x = 5 or x = -4
now we have to plug these in to see which (if any) check out...
if we do that we find that only x = 5 works...

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%287x%2B29%29=x%2B3

Squaring both sides
%287x%2B29%29=%28x%2B3%29%5E2
or 7x%2B29=x%5E2+%2B+6x+%2B+9
or x%5E2+%2B+6x+%2B+9+-+7x+-+29+=+0
or x%5E2+-+x+-+20+=+0
or x%5E2+-+5x+%2B+4x+-+20+=+0
or x%28x+-+5%29+%2B+4%28x+-+5%29+=+0
or %28x%2B4%29%28x-5%29=0

Hence either (x + 4) = 0 i.e. x = -4 or (x - 5) = 0 i.e. x = 5.

So either x = -4 or x = 5.