Question

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 \( x^3 - 10 = -2 \).