X2-18=7x

To solve the equation \( x^2 - 18 = 7x \), we first rearrange the equation to set it to zero: 1. Move all terms to one side of the equation: \[ x^2 - 7x - 18 = 0 \] Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. Let's attempt to factor it first. We need to find two numbers that multiply to \(-18\) (the constant term) and add to \(-7\) (the coefficient of \(x\)). The numbers \(-9\) and \(2\) fit this requirement: \[ (x - 9)(x + 2) = 0 \] Now, we set each factor equal to zero: 1. \( x - 9 = 0 \) \(\Rightarrow x = 9\) 2. \( x + 2 = 0 \) \(\Rightarrow x = -2\) Thus, the solutions to the equation \( x^2 - 18 = 7x \) are: \[ x = 9 \quad \text{and} \quad x = -2 \]