How to solve this word problem

Translate the words into an equation:

a number is subtracted from 31:

31 - n

the principle square root of this difference:

sqrt(31 - n)

equals:

=

the number decreased by 1

n - 1

Combine:

sqrt(31 - n) = n - 1

Square both sides:

31 - n = (n - 1)(n - 1)

Multiply out the right side:

31 - n = n^2 - 2n + 1

Add n to both sides:

31 = n^2 - n + 1

Put into quadratic form by subtracting 31 from both sides:

n^2 - n - 30 = 0

Factor to:

(n - 6)(n + 5) = 0


n is either 6 or -5

sqrt(31-N) = N-1
31-N = N^2 -2N + 1
N^2 - N - 30 = 0
(N - 6)(N + 5) = 0

the possible solutions are 6 and -5. Since the principle square root is positive, the answer is 6.

Jim

sqrt(31-x)=x-1
31-x=(x-1)^2
x^2-2x+1+x-31=0
x^2-x-30=0
(x-6)(x+5)=0
x=-5
x=6

proof sqrt31-(-5)=6
-5-1=-6 (no solution)

sqrt31+5=6
5+1=6
only x=5 is solution

The numbers are 6 and -5