can you solve this?

Question

if 6 is added to the square of a number, the result is 22. find all such numbers.

and

The product of the page numbers on two facing pages of a book is 600. find the page numbers.

Answer 1

Question 1
x² + 6 = 22
x² = 16
x = ± 4

Question 2
x(x + 1) = 600
x² + x - 600 = 0
(x + 25)(x - 24) = 0
x = 24
Page numbers are 24 and 25

Answer 2

The trick is just to set up the equations correctly

x^2 + 6 = 22 so x^2 = 16 so x = +/- Sqrt(16)=+/- 4

Second one the two numbers have to be consecutive so
x(x+1)=600 so x^2 +x =600 so x^2 + x -600 = 0
Now use the quadratic formula. You have to use the positive answear you get which is x=24. So the pages are 24 and 25.

Answer 3

So you have a number; let's call it N.
6 is added to the square of a number can be written as:
6+N^2
you know this equals 22 so
6+N^2=22
Solve for N
subtract 6 from both sides
N^2= 16
Square Root both sides
N= plus or minus 4


Second Problem:
So you have one page. Then you have the next page.
The first page let's call P.
The next page would be P+1

therefore their product can be written as
P(P+1)
You know this equals 600 so:
P(P+1)=600
expand both sides
P^2+P=600
Subtract each side by 600
P^2+P-600=0
(P+25)(P-24)=0
set each equal to 0
P+25=0 and P-24=0

Solve for P in each.
P=-25
P= 24

you can't have negative page numbers so the one you want is Page is 24.

So the next page is P+1 = 25