Решите неравенство - x^2-x+55> = (x-4) ^2

-x^2 - x + 55 > = (x - 4) ^2;

Раскроем скобки.

-x^2 - x + 55 > = x^2 - 2 * 4 * x + 4^2;

-x^2 - x + 55 > = x^2 - 8 * x + 16;

-x^2 - x^2 - x + 8 * x + 55 - 16 > = 0;

x^2 * (-1 - 1) - x * (8 - 1) + 39 > = 0;

-2 * x^2 - 7 * x + 39 > = 0;

- (2 * x^2 + 7 * x - 39) > = 0;

2 * x^2 + 7 * x - 39 < = 0;

2 * x^2 + 7 * x - 39 = 0;

D = b^2 - 4 * a * c = 7^2 - 4 * 2 * (-39) = 49 + 8 * 39 = 49 + 312 = 361 = 19^2;

x1 = (-7 + 19) / (2 * 2) = 12/4 = 3;

x2 = (-7 - 19) / 4 = - 28/4 = - 7;

Отсюда получаем, - 7 < = x < = 3.