public class Test {

  public static double func(double x)
  {
    return Math.pow(x,x)-2.5;
  }

  public static double findRoot(double low, double high)
  {
    double middle =(low+high)/2.0;
    double midVal=func(middle);
    if (Math.abs(midVal)<1e-12) return middle;
    double lowVal=func(low);
    double highVal=func(high);
    if (Math.signum(lowVal)==Math.signum(midVal))
      return findRoot(middle, high);
    else return findRoot(low, middle);
  }
  public static void main(String[] args) {
    System.out.println(findRoot(1.0, 2.0)); // 1.709275722503662

  }
}