Round #637

Solve: 2x squared minus 8 equals 0

To solve the equation \(2x^2 - 8 = 0\), we can follow these steps: 1. **Isolate the term with \(x^2\)**: \[ 2x^2 = 8 \] 2. **Divide both sides by 2** to simplify: \[ x^2 = 4 \] 3. **Take the square root of both sides** to solve for \(x\): \[ x = \pm \sqrt{4} \] \[ x = \pm 2 \] So, the solutions are: \[ x = 2 \quad \text{and} \quad x = -2 \]

To solve the equation \(2x^2 - 8 = 0\), we can follow these steps: 1. Rearrange the equation to isolate \(x^2\). 2. Solve for \(x\) by taking the square root of both sides. Let's implement this in C# using basic arithmetic operations and error handling. ```csharp using System; class Program { static void Main() { try { // Coefficients from the equation 2x^2 - 8 = 0 double a = 2; double b = 0; // Since there's no x term, b is 0 double c = -8; // Calculate the discriminant (b^2 - 4ac) double discriminant = Math.Pow(b, 2) - 4 * a * c; if (discriminant < 0) { Console.WriteLine("No real solutions."); } else { // Calculate the two possible values of x double sqrtDiscriminant = Math.Sqrt(discriminant); double x1 = (-b + sqrtDiscriminant) / (2 * a); double x2 = (-b - sqrtDiscriminant) / (2 * a); Console.WriteLine($"The solutions are: x1 = {x1}, x2 = {x2}"); } } catch (Exception ex) { Console.WriteLine($"An error occurred: {ex.Message}"); } } } ``` ### Explanation: 1. **Coefficients**: The equation \(2x^2 - 8 = 0\) can be rewritten as \(2x^2 + 0x - 8 = 0\). Here, the coefficients are: - \(a = 2\) - \(b = 0\) - \(c = -8\) 2. **Discriminant**: The discriminant \(\Delta\) of a quadratic equation \(ax^2 + bx + c = 0\) is given by \(\Delta = b^2 - 4ac\). For our equation, the discriminant is: \[ \Delta = 0^2 - 4 \cdot 2 \cdot (-8) = 64 \] 3. **Solutions**: If the discriminant is non-negative, we can find the solutions using the quadratic formula \(x = \frac{-b \pm \sqrt{\Delta}}{2a}\). For our equation: - \(x_1 = \frac{-0 + \sqrt{64}}{2 \cdot 2} = \frac{8}{4} = 2\) - \(x_2 = \frac{-0 - \sqrt{64}}{2 \cdot 2} = \frac{-8}{4} = -2\) 4. **Error Handling**: The code includes basic error handling to catch and display any exceptions that might occur during the calculation. This implementation is straightforward and follows standard C# practices for solving quadratic equations.