The next step is to solve the cubic equation. It may not have a simple solution, and finding the exact root may involve using numerical methods or calculators. Alternatively, the equation can be manipulated further to try and factorize it into simpler expressions.
To find the value of x that satisfies the equation (x+3)³ = 1, we first need to simplify the left side of the equation by expanding the cube of (x+3):
(x+3)³ = (x+3)(x+3)(x+3)
= (x+3)(x² + 6x + 9)
= x³ + 9x² + 18x + 9
Now, we have the equation:
x³ + 9x² + 18x + 9 = 1
Simplify further:
x³ + 9x² + 18x + 9 - 1 = 0
x³ + 9x² + 18x + 8 = 0
The next step is to solve the cubic equation. It may not have a simple solution, and finding the exact root may involve using numerical methods or calculators. Alternatively, the equation can be manipulated further to try and factorize it into simpler expressions.