SOLUTION: Solve the equation x+3=the square root of 7x+29 and check for extraneous roots

Algebra ->  Equations -> SOLUTION: Solve the equation x+3=the square root of 7x+29 and check for extraneous roots       Log On


   

Question 286530: Solve the equation x+3=the square root of 7x+29 and check for extraneous roots

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation x+3=the square root of 7x+29 and check for extraneous roots
3x + 3 = sqrt%287x%2B29%29
Square both sides
(3x + 3)^2 = 7x + 29
FOIL the left
9x^2 + 18x + 9 = 7x + 29
:
9x^2 + 18x - 7x + 9 - 29 = 0
:
9x^2 + 11x - 20 = 0
Factor
(9x + 20)(x - 1) = 0
Two solutions
9x = -20
x = %28-20%29%2F9
x = -2.222
and
x = +1
:
Check both solutions in the original equation
x = -2.222 is extraneous
x = 1 is a solution