Question 255553
{{{sqrt(x+5) + sqrt(x-3) = 4}}}

When you are solving a problem with two square roots, you always want to start by rearranging the formula to have one square root on each side:

{{{sqrt(x+5) = 4 - sqrt(x-3)}}}

Now we square both sides:

{{{(sqrt(x+5))^2 = (4 - sqrt(x-3))^2}}}

{{{x+5 = (4-sqrt(x-3))(4-sqrt(x-3))}}}

{{{x+5 = 16 - 8sqrt(x-3) + x - 3}}}

Now, we combine like terms and isolate the one remaining square root:

{{{x+5 = x+13-8sqrt(x-3)}}}

{{{-8 = -8sqrt(x-3)}}}

{{{1 = sqrt(x-3)}}}

And now we square both sides again:

{{{1 = x-3}}}

{{{x = 4}}}

The last step is to check our answer:

{{{sqrt(4+5) + sqrt(4-3) = 4}}}
{{{3 + 1 = 4}}}

So x=4 is a valid solution.