Final answer:
To solve the equation x³ = -64, we use the sum of cubes formula to factor the equation and find the values of x that make it true. The solutions are x = -4 and x = 2.
Step-by-step explanation:
To solve the equation x³ = -64, we need to find the value of x that makes the equation true. We can rewrite the equation as x³ + 64 = 0. By using the sum of cubes formula, a³ + b³ = (a + b)(a² - ab + b²), we can factor the equation as (x + 4)(x² - 4x + 16) = 0.
To find the possible values of x, we set each factor equal to zero, giving us x + 4 = 0 and x² - 4x + 16 = 0. By solving these equations, we find that the values of x that make the equation true are x = -4 and x = 2. Therefore, the correct answer is option B.
The question asks for the value of x that makes the equation x³ = -64 true. To solve this, we need to find the cube root of -64. Remember that when you take the cube root of a negative number, the result is also negative. The cube root of 64 is 4 because 4× 4× 4 = 64. Since we are looking for the cube root of -64, the answer is -4 which is negative. Therefore, the correct answer is C. -4.