Final answer:
To solve the problem, we can set up an equation and use the quadratic formula to find the values of x. The possible values for x are 5 and 6.
Step-by-step explanation:
To solve this problem, we can set up an equation based on the given information. Let's call the number x. According to the question, if x is subtracted from 31, the principal square root of this difference is equal to the number decreased by 1. So, we have the equation:
√(31 - x) = x - 1
To solve this equation, we can square both sides to eliminate the square root:
31 - x = (x - 1)^2
Expanding and simplifying the right side of the equation, we get:
31 - x = x^2 - 2x + 1
Now, we can rearrange the equation to form a quadratic equation:
x^2 - 3x + 30 = 0
Using the quadratic formula, we can solve for x:
x = (-(-3) ± √((-3)^2 - 4*1*30))/(2*1)
After simplifying, we get two possible values for x:
x = 5 or x = 6