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=1.7 x equals 1.7 x=3.7 x equals 3.7

1 answer

To find the solutions to the quadratic equation −x^2+x=−10, we need to set the equation equal to 0:

−x^2+x+10=0

Next, we can solve this equation using the quadratic formula:

x = (-b ± √(b^2-4ac))/(2a)

In this equation, a = -1, b = 1, and c = 10. Substituting these values into the quadratic formula, we have:

x = (-(1) ± √((1)^2-4(-1)(10)))/(2(-1))
x = (-1 ± √(1+40))/(-2)
x = (-1 ± √41)/(-2)

Rounded to the nearest hundredth, the solutions are approximately x = 0.77 and x = -2.77. Therefore, the correct solution from the given options is x = 0.77.