X2-15=2x

To solve the equation \( x^2 - 15 = 2x \), first, let's rearrange it into a standard quadratic form: 1. Move all terms to one side of the equation: \[ x^2 - 2x - 15 = 0 \] 2. Now, we can factor the quadratic equation. We need two numbers that multiply to \(-15\) and add to \(-2\). The numbers \(-5\) and \(3\) fit this requirement. Therefore, we can factor the equation as: \[ (x - 5)(x + 3) = 0 \] 3. Set each factor equal to zero to solve for \(x\): \[ x - 5 = 0 \quad \Rightarrow \quad x = 5 \] \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \] So, the solutions to the equation \( x^2 - 15 = 2x \) are: \[ x = 5 \quad \text{and} \quad x = -3 \]