Question

the sqrt(9x=55) =x+5
what is x

Answer 1

square both sides and solve for x in the quadratic equation, \[x^{2}+x-30\]. the solutions being 5 and -6. now resubstitute back in the old equation, u'll get to notice that x=-6 is not a valid root because sqrt(any expresion) is always +ve and hence the value of x is 5 only :)

Answer 2

got it ?

Answer 3

wen u substitute x=-6 in the equation u gave , we get \[\sqrt{1}\] = -1 which is wrong. hence x=-6 is not the corect answer. this root comes up because the given equation is linear(as in the highest power of x is one) and hence only one root is present. wen u square u increase the power of x to 2 and hence u get 2 roots. but primary equation has only one. so to eliminate the wrong value u substitue back to check for mathematical correctness :)
ps:its a long mail i know , but i explains an important concept