1. x(x-4)=60

2. (x+1)²+(x-8)²=45

Answer:Let's solve these equations step by step: 1. x(x-4) = 60 - Expand the equation: x² - 4x = 60- Move all terms to one side: x² - 4x - 60 = 0- Factor the quadratic equation: (x - 10)(x + 6) = 0- Solve for x:- x - 10 = 0 => x = 10- x + 6 = 0 => x = -6 Therefore, the solutions are x = 10 and x = -6 2. (x+1)² + (x-8)² = 45 - Expand the squares: x² + 2x + 1 + x² - 16x + 64 = 45- Combine like terms: 2x² - 14x + 20 = 0- Simplify by dividing by 2: x² - 7x + 10 = 0- Factor the quadratic equation: (x - 5)(x - 2) = 0- Solve for x:- x - 5 = 0 => x = 5- x - 2 = 0 => x = 2 Therefore, the solutions are x = 5 and x = 2

Answered by buntogchelmie | 2024-09-02