How do you solve x^{2}+(x+1)^{2}=25?

1 Answer
Mar 27, 2017

x= -4, 3

Explanation:

x^2 + (x+1)^2 = 25
x^2 + (x+1)(x+1) = 25
x^2 + x^2+2x+1 = 25
2x^2 +2x-24 = 0 (Divide by a 2)
x^2 +x-12 = 0
(x+4)(x-3)=0
x+4= 0
x-3=0
x= -4, 3

Plug in to make sure:
x^2 + (x+1)^2 = 25
-4^2 + (-4+1)^2 = 25
16 + 9 = 25
25=25

3^2 + (3+1)^2 = 25
9 + 16 = 25
25=25

Both are correct, so x = -4 and 3