Question 135510
{{{sqrt(3x+4)-sqrt(2x+1)=1}}} Start with the given equation



{{{sqrt(3x+4)=1+sqrt(2x+1)}}} Add {{{sqrt(2x+1)}}} to both sides



{{{sqrt(3x+4)=1+sqrt(2x+1)}}} Add {{{sqrt(2x+1)}}} to both sides



{{{3x+4=(1+sqrt(2x+1))^2}}} Square both sides



{{{3x+4=1+2*sqrt(2x+1)+2x+1}}} Foil the right side



{{{3x+4=2*sqrt(2x+1)+2x+2}}} Combine like terms



{{{3x+4-2x-2=2*sqrt(2x+1)}}} Subtract 2x from both sides. Subtract 2 from both sides.


{{{x+2=2*sqrt(2x+1)}}} Combine like terms 



{{{(x+2)^2=4*(2x+1)}}} Square both sides



{{{x^2+4x+4=4*(2x+1)}}} Foil the left side



{{{x^2+4x+4=8x+4}}} Distribute



{{{x^2+4x+4-8x-4=0}}}  Subtract 8x from both sides.  Subtract 4 from both sides. 



{{{x^2-4x=0}}} Combine like terms



{{{x(x-4)=0}}} Factor the left side 




Now set each factor equal to zero:

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


{{{x=0}}} or  {{{x=4}}}    Now solve for x in each case



So our answers are


 {{{x=0}}} or  {{{x=4}}}