Math Quadratic Formula/Factoring Solve this equation

the question is radical(x + 10) + radical(3 - x) =5
and the answer is not "no real solutions"
What is the correct answer?

√(x + 10) + √(3 - x) = 5
(√(x + 10) + √(3 - x))^2 = 5^2
x + 10 + 2√(3x - x^2 + 30 - 10x) + 3 - x = 25
13 + 2√(-x^2 - 7x + 30) = 25
2√(-x^2 - 7x + 30) = 12
√(-x^2 - 7x + 30) = 6
(√(-x^2 - 7x + 30))^2 = 6^2
-x^2 - 7x + 30 = 36
0 = x^2 + 7x + 6
0 = (x + 6)(x + 1)
x = -6 or x = -1
Verify neither is an extraneous solution:
√(-6 + 10) + √(3 - x) =
√4 + √9 =
2 + 3 = 5
√(-1 + 10) + √(3 - -1) =
√9 + √4 =
3 + 2 =
5