Question 62209
{{{sqrt(2x+4)=sqrt(x+3)+1}}}

Square both sides: {{{2x+4 = (x+3)+2sqrt(x+3)+1}}}.
Subtract x+4 from both sides: {{{x = 2sqrt(x+3)}}}.
Square both sides: {{{x^2 = 4(x+3)}}}.
Turn the equation into a quadratic: {{{x^2-4x-12 = 0}}}.
This factors: {{{(x-6)(x+2)= 0}}}.
So, x=6 and x=-2 are possible solutions.

Let's check the possible solutions:

When x=6, {{{sqrt(2x+4)=sqrt(16) = 4}}} and {{{sqrt(x+3)+1 = sqrt(9)+1 = 4}}}.
When x=-2, {{{sqrt(2x+4)=sqrt(0) = 0}}} and {{{sqrt(x+3)+1 = sqrt(1)+1 = 2}}} so x= -2 is not an answer.

So, the only answer is x=6.