Solve the equation

(x-3)^2+(x+2)^2=17

(X-3)^2 + (X + 2)^2 = 17

X^2 - 6X + 9 + X^2 +4X + 4 = 17
Combine like - terms.
2X^2 - 2X + 13 = 17
Set Eq. = 0
2X^2 - 2X - 4 = 0
Divide both sides by 2
X^2 - X - 2 = 0.
Factor EQ.
( X - 2 ) ( X + 1 ) = 0
X - 2 = 0. X = 2; X + 1 = 0, X = - 1 .
Solution set: X = 2, and x = - 1 .