Equation transformable to quadratic equationsolve1:3x(x-6)-42=62:x(x+3)-7=0
Answer (1)
Answer:Let's solve these equations step-by-step:**1. 3x(x-6) - 42 = 6*** **Expand:** First, distribute the 3x: 3x² - 18x - 42 = 6* **Simplify:** Move all terms to one side to get a standard quadratic equation: 3x² - 18x - 48 = 0* **Divide by 3:** Divide the entire equation by 3 to simplify: x² - 6x - 16 = 0* **Factor:** Factor the quadratic expression: (x - 8)(x + 2) = 0* **Solve for x:** Set each factor equal to zero and solve: x - 8 = 0 or x + 2 = 0 x = 8 or x = -2**Therefore, the solutions to the equation 3x(x-6) - 42 = 6 are x = 8 and x = -2.****2. x(x+3) - 7 = 0*** **Expand:** Distribute the x: x² + 3x - 7 = 0* **Quadratic Formula:** This equation doesn't factor easily, so we'll use the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a Where a = 1, b = 3, and c = -7* **Substitute and Solve:** x = [-3 ± √(3² - 4 * 1 * -7)] / (2 * 1) x = [-3 ± √(37)] / 2**Therefore, the solutions to the equation x(x+3) - 7 = 0 are x = (-3 + √37) / 2 and x = (-3 - √37) / 2.**
