To solve the quadratic equation \(-x^2 + x = -10\), we first rearrange it into standard form:
\[ -x^2 + x + 10 = 0 \]
Next, we can multiply the entire equation by \(-1\) to simplify it:
\[ x^2 - x - 10 = 0 \]
Now, we can use the quadratic formula to find the solutions, where \(a = 1\), \(b = -1\), and \(c = -10\):
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Substituting in the values:
\[ x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-10)}}{2(1)} \]
Calculating inside the square root:
\[ x = \frac{1 \pm \sqrt{1 + 40}}{2} \] \[ x = \frac{1 \pm \sqrt{41}}{2} \]
Calculating \(\sqrt{41}\):
\[ \sqrt{41} \approx 6.403 \]
Now substituting back to find \(x\):
\[ x = \frac{1 + 6.403}{2} \quad \text{and} \quad x = \frac{1 - 6.403}{2} \] \[ x \approx \frac{7.403}{2} \approx 3.7015 \quad \text{and} \quad x \approx \frac{-5.403}{2} \approx -2.7015 \]
Thus, rounding \(3.7015\) to the nearest hundredth gives \(3.70\).
So the solution to the quadratic equation \(-x^2+x=-10\) is approximately:
\[ x \approx 3.70 \]
Among the provided options, \(x = 3.7\) (or \(x\) equals \(3.7\)) is the correct answer.