Which of the following is a solution to the quadratic equation −x2+x=−10

Question

? 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 can rearrange it to the standard form of a quadratic equation: x^2 - x + 10 = 0.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac))/2a, where a = 1, b = -1, and c = 10, we can plug in the values and solve for x.

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

Calculating the discriminant, √(1 - 40), we get a negative value under the square root. This means that there are no real solutions to the quadratic equation.

Thus, none of the given options (0.77, 0.27, 1.7, 3.7) are solutions to the quadratic equation −x^2 + x = −10.