Question

Which of the following is a solution to the quadratic equation −x2+x=−10 ? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)
Responses

x=0.77
x equals 0.77

x=0.27
x equals 0.27

x=3.7
x equals 3.7

x=1.7
x equals 1.7

Answer 1

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**