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

Answer 1

To solve the quadratic equation \(-x^2 + x = -10\), we can rearrange it into standard form:

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

Multiplying through by -1 to make the leading coefficient positive gives us:

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

Now we can use the quadratic formula, which is:

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

where \(a = 1\), \(b = -1\), and \(c = -10\).

Calculating the discriminant:

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

Now substitute back into the quadratic formula:

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

Calculating \(\sqrt{41}\), which is approximately 6.403:

\[
x = \frac{1 \pm 6.403}{2}
\]

This gives us two potential solutions:

1. \(x = \frac{1 + 6.403}{2} = \frac{7.403}{2} \approx 3.7015\)
2. \(x = \frac{1 - 6.403}{2} = \frac{-5.403}{2} \approx -2.7015\)

Rounding to the nearest hundredth,

1. \(x \approx 3.70\)
2. \(x \approx -2.70\)

Out of the provided options, the closest solution is:

**x = 3.7**.