Which of the following is a solution to the quadratic equation −x2+x=−10%0D%0A−%0D%0A%0D%0A2%0D%0A+%0D%0A%0D%0A=%0D%0A−%0D%0A10%0D%0A ? Assume that the solution has been rounded to the nearest hundredth, if applicable.

Answer 1

To solve the quadratic equation −x^2+x=−10 , we need to set the equation equal to zero by subtracting -10 from both sides:

−x^2 + x + 10 = 0.

To find the solutions, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a).

For this equation, a = -1, b = 1, and c = 10.

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 ≈ (-1 + √41)/(-2) ≈ 2.19
x ≈ (-1 - √41)/(-2) ≈ -1.19

Therefore, the solutions to the quadratic equation −x^2+x=−10 are approximately x = 2.19 and x = -1.19.