which of the following is a solution to the quadratic equation -x^2+x=-10? assume that the solution has been rounded to the nearest hundredth, if applicable
x=0.27
x=3.7
x=1.7
x=0.77
To solve the quadratic equation, we set -x^2 + x = -10 equal to zero:
-x^2 + x + 10 = 0
Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = -1, b = 1, and c = 10.
Plugging in the values, we get:
x = (-1 ± √(1^2 - 4(-1)(10)))/(2(-1))
x = (-1 ± √(1 + 40))/(-2)
x = (-1 ± √41)/(-2)
Using the quadratic formula, we get two possible solutions: x = (-1 + √41)/(-2) and x = (-1 - √41)/(-2).
Rounding to the nearest hundredth gives x ≈ 0.27 and x ≈ 3.7.
Therefore, the solutions are x = 0.27 and x = 3.7.
None of the answer options provided include the second solution of x ≈ 3.7, so the correct answer is x = 0.27.