To find the solutions to the quadratic equation \(-x^2 + x = -10\), we first rearrange it into standard form:
\[ -x^2 + x + 10 = 0 \]
Multiplying the entire equation by -1 to make the leading coefficient positive gives us:
\[ x^2 - x - 10 = 0 \]
Next, we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 1\), \(b = -1\), and \(c = -10\).
Calculating the discriminant:
\[ b^2 - 4ac = (-1)^2 - 4 \cdot 1 \cdot (-10) = 1 + 40 = 41 \]
Now we can find \(x\):
\[ x = \frac{-(-1) \pm \sqrt{41}}{2 \cdot 1} = \frac{1 \pm \sqrt{41}}{2} \]
Calculating \(\sqrt{41}\) gives us approximately \(6.4\). Therefore:
\[ x = \frac{1 + 6.4}{2} \quad \text{and} \quad x = \frac{1 - 6.4}{2} \]
Calculating these two values:
- \(x = \frac{7.4}{2} \approx 3.7\)
- \(x = \frac{-5.4}{2} \approx -2.7\)
The solutions rounded to the nearest hundredth are \(x \approx 3.7\) and \(x \approx -2.7\).
From your options, the correct solution is:
\[ \boxed{x = 3.7} \]