To solve the equation \(-x^{2.9} = -3\), we can start by eliminating the negative signs on both sides. This gives us:
\[ x^{2.9} = 3 \]
Next, to solve for \(x\), we will need to raise both sides of the equation to the power of \(\frac{1}{2.9}\):
\[ x = 3^{\frac{1}{2.9}} \]
Using a calculator, we can compute \(3^{\frac{1}{2.9}}\):
\[ x \approx 1.360 \]
Since \(x^{2.9}\) can also yield a negative value (because \(x\) can be negative), we should also consider the negative root:
\[ x = -3^{\frac{1}{2.9}} \approx -1.360 \]
Thus, the solutions for the equation \(-x^{2.9} = -3\) are:
\[ x \approx 1.360 \quad \text{and} \quad x \approx -1.360 \]