math help i dont need homework done i just want to check if its right.?

Question

these were my problems that i finished

find three consecutive positive integers such that the square of the third is 51 more than the sum of the first and second

i got -X=25 but i dont see how thats right because X has to be positive but the number in this problem has to be positive too. if you do tell me the answer please show me the work and the check.

write an equation of the line whose slope is -2 and whose y intercept is -1

i got y= -2X+-1

thank you.

Answer 1

PROBLEM 1:

Let the three positive integers be:
x, x + 1, x + 2

(x+2)² = x + (x + 1) + 51
(x+2)² = 2x + 52

Expand the left hand side with FOIL:
x² + 4x + 4 = 2x + 52

Now get everything on the left:
x² + 2x - 48 = 0

Factor this:
(x + 8)(x - 6) = 0

So x = -8 or x = 6

But obviously -8 can't be an answer, so the answer is the first number is 6.

The numbers are 6, 7 and 8.

Double-check
8² = 6 + 7 + 51

PROBLEM 2:

You are exactly correct, though rather than +-1, just write:
y = -2x - 1

Answer 2

let x = first integer
x +1 = second interger
x + 2 = third integer

x + x+1 = (x+2)^2 - 51
2x +1 = x^2 +4x +4 -51
x^2 +2x - 48 =0
(x - 6)(x + 8) = 0
x = -8 ; x = 6
so, the three postive integers are 6,7 and 8

yes, the equation is correct....