Final answer:
The solutions to the equation x^2 + 49 = x + 5 are x = -6 or x = -3.
Step-by-step explanation:
To solve the equation x^2 + 49 = x + 5, we can rearrange it into a quadratic equation: x^2 - x - 44 = 0. Now, we can use the quadratic formula to find the solutions for x:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values from our equation, we get:
x = (1 ± √(1 - 4(-44))) / 2
After simplifying, we find that x equals -6 or x equals -3. Therefore, the solution to the equation x^2 + 49 = x + 5 is x = -6 or x = -3.