SOLUTION: I need to find all real or imaginary solutions to this equation. Use the method of your choice. √7x+29 = x + 3 note: sqrt extends over 7x

Algebra ->  Equations -> SOLUTION: I need to find all real or imaginary solutions to this equation. Use the method of your choice. √7x+29 = x + 3 note: sqrt extends over 7x      Log On


   

Question 309012: I need to find all real or imaginary solutions to this equation.
Use the method of your choice.
√7x+29 = x + 3 note: sqrt extends over 7x+29
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Use the method of your choice.
sqrt%287x%2B29%29 = x + 3
Square both sides
7x + 29 = (x + 3)^2
FOIL the right sides
7x + 29 = x^2 + 6x + 9
Combine like terms on the right
0 = x^2 + 6x - 7x + 9 - 29
A quadratic equation
x^2 - x - 20 = 0
Factors to
(x-5)(x+4) = 0
two solutions
x = +5
x = -4
;
check both solution in original equation
x = 5
sqrt%287%285%29%2B29%29 = 5 + 3
sqrt%2835%2B29%29 = 5 + 3
sqrt%2864%29 = 8
8 = 8, a good solution
:
x=-4
sqrt%287%28-4%29%2B29%29 = -4 + 3
sqrt%28-28%2B29%29 = -4 + 3
sqrt%281%29 = -1
+1 does not = -1, not a good solution