Round #552

Solve: 2x squared minus 8 equals 0

To solve the equation 2x^2 - 8 = 0, we can follow these steps: 1. Add 8 to both sides of the equation: 2x^2 - 8 + 8 = 0 + 8 2x^2 = 8 2. Divide both sides of the equation by 2: 2x^2 / 2 = 8 / 2 x^2 = 4 3. Take the square root of both sides of the equation: x = ±√4 x = ±2 So, the solutions to the equation 2x^2 - 8 = 0 are x = 2 and x = -2. Here is the C# code to solve this equation: ```csharp using System; class Program { static void Main() { // Define the coefficients of the quadratic equation double a = 2; double b = 0; double c = -8; // Calculate the solutions using the quadratic formula double x1 = (-b + Math.Sqrt(b * b - 4 * a * c)) / (2 * a); double x2 = (-b - Math.Sqrt(b * b - 4 * a * c)) / (2 * a); // Print the solutions Console.WriteLine("The solutions are x = " + x1 + " and x = " + x2); } } ``` When you run this code, it will output: ``` The solutions are x = 2 and x = -2 ```

```csharp using System; class Program { static void Main() { // Define the coefficients of the quadratic equation double a = 2; double b = 0; double c = -8; // Calculate the roots of the quadratic equation double root1 = (-b + Math.Sqrt(b * b - 4 * a * c)) / (2 * a); double root2 = (-b - Math.Sqrt(b * b - 4 * a * c)) / (2 * a); // Print the roots Console.WriteLine("The roots of the equation are: " + root1 + " and " + root2); } } ``` This C# program solves the quadratic equation 2x^2 - 8 = 0. The equation is in the form ax^2 + bx + c = 0, where a = 2, b = 0, and c = -8. The program uses the quadratic formula to calculate the roots of the equation, which are then printed to the console. The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a In this case, since b = 0, the formula simplifies to: x = ±√(-c / a) Plugging in the values of a and c, we get: x = ±√(8 / 2) x = ±√4 x = ±2 Therefore, the roots of the equation are x = 2 and x = -2.