Put the correct steps in to solve the equation: x^3−10=−2 And how many solution(s) is there?

Answer 1

To solve the equation \( x^3 - 10 = -2 \), we will follow these steps:

1. Isolate the cubic term: \[ x^3 - 10 = -2 \] Adding 10 to both sides gives: \[ x^3 = -2 + 10 \] \[ x^3 = 8 \]

2. Take the cube root: We take the cube root of both sides: \[ x = \sqrt[3]{8} \]

3. Simplify the cube root: Since \( \sqrt[3]{8} = 2 \), we find: \[ x = 2 \]

Number of Solutions:

The equation \( x^3 = 8 \) is a cubic equation, and because the greatest power of x is 3, there is generally one real solution. In this case, we can also see that \( x = 2 \) is the only real solution.

Conclusion:

So, the final solution is: \[ x = 2 \] There is one real solution to the equation \( x^3 - 10 = -2 \).