Question

Find the solution to the quadratic equation −x^2+x=−10

Assume that the solution has been rounded to the nearest hundredth, if applicable.

(1 point)
Responses

x= 0.77
x= 0.77

x = 0.27
x = 0.27

x = 1.7
x = 1.7

x = 3.7

Answer 1

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 will use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 1\), \(b = -1\), and \(c = -10\).

First, we calculate the discriminant:

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

Now, substituting the values into the quadratic formula:

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

Now, we calculate \(\sqrt{41}\):

\[
\sqrt{41} \approx 6.403
\]

Now we can find the two potential solutions for \(x\):

\[
x_1 = \frac{1 + 6.403}{2} \approx \frac{7.403}{2} \approx 3.7015
\]
\[
x_2 = \frac{1 - 6.403}{2} \approx \frac{-5.403}{2} \approx -2.7015
\]

Rounding \(x_1\) to the nearest hundredth:

\[
x_1 \approx 3.70
\]

So the solutions to the quadratic equation are \(x \approx 3.70\) and \(x \approx -2.70\). Based on the responses provided, the closest answer is:

\[
\text{x = 3.7}
\]