Question 92162
{{{sqrt(2+x)=x}}}
Square both sides of the equation:
{{{x+2=x^2}}}
Put the equation in standard form:
{{{x^2-x-2=0}}}
Factor:
{{{(x-2)(x+1)=0}}}
Equate each factor to 0 and solve for x:
{{{x-2=0}}}
{{{x=2}}}
{{{x+1=0}}}
{{{x=-1}}}
Now, you need to plug these results back into the original equation to see if it still holds true. You can see that x=2 is a valid answer, since the equation holds when you plug that one in. However, x=-1 does not hold true. That is called an "extraneous root." It's a result of solving the problem, but it is not a valid answer. The only correct answer is:
{{{highlight(x=2)}}}
Good Luck,
tutor_paul@yahoo.com