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=1.7 x equals 1.7 x=0.77 x equals 0.77 x=0.27 x equals 0.27 x=3.7 x equals 3.7

Answer 1

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 through by -1 to make \( x^2 \) positive, we get:

\[
x^2 - x - 10 = 0
\]

Now, we can use the quadratic formula to find the solutions, where the quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For our equation \( x^2 - x - 10 = 0 \), we have:
- \( a = 1 \)
- \( b = -1 \)
- \( c = -10 \)

Now, we can calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = (-1)^2 - 4(1)(-10) = 1 + 40 = 41
\]

Next, we apply the quadratic formula:

\[
x = \frac{-(-1) \pm \sqrt{41}}{2(1)} = \frac{1 \pm \sqrt{41}}{2}
\]

Calculating the two possible values for \( x \):

1. \( x_1 = \frac{1 + \sqrt{41}}{2} \)
2. \( x_2 = \frac{1 - \sqrt{41}}{2} \)

Calculating \( \sqrt{41} \) (approximately 6.4):

1. \( x_1 \approx \frac{1 + 6.4}{2} = \frac{7.4}{2} = 3.7 \)
2. \( x_2 \approx \frac{1 - 6.4}{2} = \frac{-5.4}{2} \approx -2.7 \)

Now, we round \( x_1 \) to the nearest hundredth and we get:

\[
x_1 \approx 3.7
\]

Thus, the solution to the quadratic equation \( -x^2 + x = -10 \) rounded to the nearest hundredth is:

\[
\boxed{3.7}
\]