x^2 + (x+3)^2 = (x+6)^2
From Binomial Theorem
=> x^2 + (x+3)^2 - (x+6)^2 = x^2 + 2(3-6)x +(3^2 - 6^2) = 0
=> x^2 -6x - 27 = 0 = (x+3)(x-9) => x = -3, 9
verify
x = -3
(-3)^2 = (3)^2 = (-3+6)^2
x = 9
(9)^2 + (3*4)^2 = 9^2 + 16*9 = 25*9 = 5^2*3^2 = (15)^2 = (9+6)^2
x^2 + (x+3)^2 = (x+6)^2
From Binomial Theorem
=> x^2 + (x+3)^2 - (x+6)^2 = x^2 + 2(3-6)x +(3^2 - 6^2) = 0
=> x^2 -6x - 27 = 0 = (x+3)(x-9) => x = -3, 9
verify
x = -3
(-3)^2 = (3)^2 = (-3+6)^2
x = 9
(9)^2 + (3*4)^2 = 9^2 + 16*9 = 25*9 = 5^2*3^2 = (15)^2 = (9+6)^2