To find the solution to the quadratic equation \(-x^2 + x = -10\), we first rearrange the equation:
\[ -x^2 + x + 10 = 0 \]
Next, we can multiply through by -1 to make the leading coefficient positive:
\[ x^2 - x - 10 = 0 \]
Now, we can apply the quadratic formula, which is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \(a = 1\), \(b = -1\), and \(c = -10\). We first calculate the discriminant:
\[ b^2 - 4ac = (-1)^2 - 4(1)(-10) = 1 + 40 = 41 \]
Now we can use the quadratic formula:
\[ x = \frac{-(-1) \pm \sqrt{41}}{2(1)} = \frac{1 \pm \sqrt{41}}{2} \]
Calculating \(\sqrt{41}\) gives approximately \(6.403\). Thus, we have two solutions:
\[ x = \frac{1 + 6.403}{2} \approx \frac{7.403}{2} \approx 3.7015 \] \[ x = \frac{1 - 6.403}{2} \approx \frac{-5.403}{2} \approx -2.7015 \]
Rounding \(3.7015\) to the nearest hundredth gives \(3.70\).
So the approximate solution rounded to the nearest hundredth is \(x \approx 3.70\).
The closest option provided is:
x = 3.7