Select the correct answer to the following equation: −x^3/2=−27
.(1 point)
Responses
9
no solution, the answer cannot be negative
−9
−3
−3
To solve the equation −x^3/2 = −27, we can begin by isolating the variable x.
First, we can multiply both sides of the equation by -2 to cancel out the exponent of 3/2:
-2 * (-x^3/2) = -2 * (-27)
This simplifies to:
x^3 = 54
Next, to solve for x, we can take the cube root of both sides of the equation:
∛(x^3) = ∛(54)
This gives us:
x = ∛(54)
Now, let's evaluate the cube root of 54:
x ≈ 3.77976314968
Therefore, the correct answer is approximately 3.78. None of the provided options (9, no solution, -9, -3) are the correct answer.