Can't seem to solve a radical equation? Question is : $sqrt{x+19} + sqrt{x-2} = 7$

So there is this equation that I've been trying to solve but keep having trouble with.

The unit is about solving Radical equations and the question says
Solve:
$$\sqrt{x+19} + \sqrt{x-2} = 7$$

I don't want the answer blurted, I want to know how it's done, including steps please.

Thank you!

Answer

$\sqrt{x+19} + \sqrt{x-2} = 7$

Squaring both sides, we have

$x+19+2\sqrt{x+19}\sqrt{x-2}+x-2=49$

Collecting terms, we have

$2x+17+2\sqrt{x^2+17x-38}=49$

$\sqrt{x^2+17x-38}=\dfrac{32-2x}{2}$

Squaring again

$x^2+17x-38=\dfrac{1024-128+4x^2}{4}$

$x^2+17x-38=256-32x+x^2$

$49x=294$

$\therefore x=\dfrac{294}{49}=6$

We can easily verify that this is a correct solution.