What are the roots of the equation √(2x + 9) = 13 - x?

Question: What are the roots of the equation √(2x + 9) = 13 - x?

Solution:
√(2x + 9) = 13 - x
Squaring both sides, we get
2x + 9 = (13 - x)²
⇒ 2x + 9 = 169 - 26x + x²
⇒ - x² + 28x - 160 = 0
⇒ x² - 28x + 160 = 0
⇒ (x - 8)(x - 20) = 0
⇒ x - 8 = 0 or x - 20 = 0
⇒ x = 8 or x = 20

But x = 20 does not satisfy the given equation, so it is rejected. Hence, the root of the given equation is 8.