Answer:
x = 7 and x = -2
Explanation:
To solve the equation 18^(x^2+4x+4) = 18^(9x+18), we can equate the exponents and solve for x.
x^2 + 4x + 4 = 9x + 18
Rearranging the terms:
x^2 + 4x - 9x + 4 - 18 = 0
Simplifying:
x^2 - 5x - 14 = 0
Now we can factor the quadratic equation:
(x - 7)(x + 2) = 0
Setting each factor equal to zero:
x - 7 = 0 or x + 2 = 0
Solving for x:
x = 7 or x = -2
Therefore, the solutions to the equation are x = 7 and x = -2.