Final answer:
To solve the equation x³ - 216 = 2(x - 6), simplify and find the value of x by factoring the equation.
Step-by-step explanation:
To solve the equation: x³ - 216 = 2(x - 6), we need to simplify and find the value of x. First, distribute 2 to x - 6, which gives us 2x - 12. Next, we can rewrite the equation as x³ - 2x + 12 - 216 = 0. Combine like terms to get x³ - 2x - 204 = 0. Now, we can factor and solve for x. After factoring, we get (x - 6)(x² + 6x + 34) = 0. Set each factor equal to zero and solve for x. The two possible values for x are x = 6 and x = -3 + √(10)i, where i is the imaginary unit.