#include <stdio.h>
#include <math.h>

#define EPSILON 1e-6
#define MAX_ITERATIONS 100

double f(double x, double a) {
    return x * x - a;
}

double bisection_method(double a, double left, double right) {
    double mid;
    int iterations = 0;

    while (right - left > EPSILON && iterations < MAX_ITERATIONS) {
        mid = (left + right) / 2;
        
        if (f(mid, a) == 0.0) {
            return mid;
        } else if (f(mid, a) * f(left, a) < 0) {
            right = mid;
        } else {
            left = mid;
        }
        
        iterations++;
    }

    return (left + right) / 2;
}

int main() {
    double a, result;

    printf("請輸入一個正數 a 來求解 x^2 = a: ");
    scanf("%lf", &a);

    if (a < 0) {
        printf("錯誤：a 必須是非負數\n");
        return 1;
    }

    result = bisection_method(a, 0, a > 1 ? a : 1);

    printf("方程 x^2 = %.6f 的解約為 x = %.6f\n", a, result);
    printf("驗證：%.6f^2 = %.6f\n", result, result * result);

    return 0;
}