The dimensions of a fish tank are x-3, x-4, and x-2. The fish tank has a volume of 23x+3 cubic units.

Question

Solve for x and find the dimensions of the tank.

Answer 1

(x-2)(x-3)(x-4) = 23x+3

(x^2-5x+6)(x-4) = 23x+3

0=

x^3 - 5x^2 + 6x

-4x^2 + 20x - 24

-23x - 3

x^3 - 9x^2 + 3x - 27 = 0

x^2(x-9) + 3(x-9) = 0

(x-9) (x^2+3) = 0

x-9 = 0 or x^2 + 3 = 0

x=9 or x = sqrt(3)*i or x = -sqrt(3)*i

x=9 is the only answer as the silly imaginaries are disqualified

(x-2)(x-3)(x-4) = 7*6*5 = 210

and

23*9+3 = 207+3=210

so yes it checks

7 by 6 by 5 has a volume of 210 cubic units