SOLUTION: Please help me solve this equation: {{{sqrt(5x+39)=x+3}}}

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Question 448614: Please help me solve this equation: sqrt%285x%2B39%29=x%2B3
Found 2 solutions by ankor@dixie-net.com, nerdybill:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation: sqrt%285x%2B39%29=x%2B3
Square both sides
%28sqrt%285x%2B39%29%29%5E2=%28x%2B3%29%5E2
:
FOIL (x+3)(x+3) on the right
5x + 39 = x^2 + 6x + 9
:
Combine like terms on the right
0 = x^2 + 6x - 5x + 9 - 39
:
A quadratic equation
x^2 + x - 30 = 0
:
Factors to
(x+6)(x-5) = 0
:
Two solutions
x = -6
x = +5
:
Check both solution in the original problem
sqrt%285%28-6%29%2B39%29=-6%2B3
:
sqrt%28-30%2B39%29=+-3
:
sqrt%289%29+=+-3
3 does not = -3, x=-6 is not a solution
:
try x=5
sqrt%2825%2B39%29=5%2B3
sqrt%2864%29+=+8: x=5 is a valid solutions

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285x%2B39%29=x%2B3
start by squaring both sides to get:
5x%2B39+=+%28x%2B3%29%5E2
5x%2B39+=+%28x%2B3%29%28x%2B3%29
FOIL the right side:
5x%2B39+=+x%5E2%2B6x%2B9
39+=+x%5E2%2Bx%2B9
0+=+x%5E2%2Bx-30
factoring the right:
0+=+%28x%2B6%29%28x-5%29
x = {-6, 5}