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
To find the solutions to the quadratic equation −x^2 + x = −10, we can rearrange the equation to form a quadratic equation of the form ax^2 + bx + c = 0. In this case, a = -1, b = 1, and c = 10.
Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, we can substitute the values of a, b, and c into the formula:
x = (-(1) ± √((1)^2 - 4(-1)(10))) / 2(-1)
x = (-1 ± √(1 + 40)) / -2
x = (-1 ± √41) / -2
Rounding to the nearest hundredth, the two solutions to the quadratic equation −x^2 + x = −10 are approximately:
x ≈ -0.73 and x ≈ 1.73