Question 131903
{{{sqrt(3x+24)=x+2}}} Start with the given equation



{{{3x+24=(x+2)^2}}} Square both sides



{{{3x+24=x^2+4x+4}}} Foil



{{{0=x^2+4x+4-3x-24}}}  Subtract 3x from both sides.  Subtract 24 from both sides. 




{{{0=x^2+x-20}}}  Combine like terms




{{{0=(x+5)(x-4)}}} Factor the right side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+5=0}}} or  {{{x-4=0}}} 


{{{x=-5}}} or  {{{x=4}}}    Now solve for x in each case



So our possible solutions are 

 {{{x=-5}}} or  {{{x=4}}} 



However, if you plug in {{{x=-5}}}, then you wont get a real solution (since you'll have a negative in the square root)




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Answer:


So the only solution is {{{x=4}}}