Solve each equation in Exercises 83–108 by the method of your choice. 9 - 6x + x^2 = 0

Key Concepts

Quadratic Equations

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. The solutions to these equations can be found using various methods, including factoring, completing the square, or applying the quadratic formula. In the given equation, 9 - 6x + x^2 = 0, it can be rearranged to the standard form to identify the coefficients.

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. For quadratic equations, this often involves finding two binomials that multiply to give the quadratic. In the context of the equation provided, factoring can simplify the process of finding the roots by setting each factor equal to zero.

Roots of an Equation

The roots of an equation are the values of the variable that satisfy the equation, making it true. For quadratic equations, the roots can be real or complex numbers, and they can be found using methods such as factoring, the quadratic formula, or graphing. Understanding how to find and interpret these roots is essential for solving the given equation effectively.