Question 103833
{{{sqrt(7x+29)=x+3}}} Start with the given equation



{{{7x+29=(x+3)^2}}} Square both sides



{{{7x+29=x^2+6x+9}}} Foil



{{{0=x^2-x-20}}} Get all terms to one side


*[invoke quadratic_formula 1, -1, -20, "x"]



Now let's plug in our possible answers back in to check




Let's check the answer x=-4


{{{sqrt(7x+29)=x+3}}} Start with the given equation



{{{sqrt(7(-4)+29)=-4+3}}} Plug in {{{x=-4}}}



{{{1=-1}}} Simplify. Since this is not true, x=-4 is not a solution





Now let's check the answer x=5


{{{sqrt(7x+29)=x+3}}} Start with the given equation



{{{sqrt(7(5)+29)=5+3}}} Plug in {{{x=5}}}



{{{8=8}}} Simplify. Since this is true, x=5 is a solution




So our only solution is x=5