Question 191751
{{{sqrt(2x+11)=x+4}}} Start with the given equation.



{{{2x+11=(x+4)^2}}} Square both sides



{{{2x+11=x^2+8x+16}}} FOIL



{{{0=x^2+8x+16-2x-11}}} Get everything to the right side



{{{0=x^2+6x+5}}} Combine like terms.



{{{0=(x+5)(x+1)}}} Factor



{{{x+5=0}}} or {{{x+1=0}}} Set each factor equal to zero



{{{x=-5}}} or {{{x=-1}}} Solve



So the <i>possible</i> solutions are {{{x=-5}}} or {{{x=-1}}}



However, if you plug in {{{x=-5}}}, you'll find that it is NOT a solution



So the only solution is {{{x=-1}}}