While practicing math for the SAT, I came across the question-
What is the sum of the solutions to $\sqrt{3x+13} = x+3$?
The first step I did was to make it a quadratic from the given equation.
Working with the quadratic, $x^2 + 3x -4$, I factored it down to $(x+4)(x-1)$.
I then checked each solution with the original equation. For $x=1$, I found the equation to hold true as $\sqrt{(3*1)+13} = 1+3$
My question then comes from when I tried to check $x=-4$.
$\sqrt{(3*-4)+13} = -4+3$
$\sqrt{(-12)+13} = -1$
$\sqrt{1} = -1$ (Or so I thought)
The answer to the problem was 1 as it did not include $x=-4$ to be a proper solution. Upon seeing this, I decided to do some research.
According to the book, Algebra, by I.M. Gelfand, Alexander Shen:
"To be exact, a square root of a nonnegative number $a$ is a nonnegative number whose square is equal to $a$"
For example: $\sqrt{25} = 5$ and $5^2 = 25$
What confuses me is why we cannot also include $-5$ as a solution to the square root, because $-5^2 = 25$