Solve equation x2-x = 0.

On the left side of the equation, x2-x can be decomposed into factors: x2-x = x (x- 1), so:

X = 0 or X- 1 = 0. So x- 1=0. = 0，X2 = 1。

In the above solving process, it is not necessary to reduce the order without square root, but to decompose the equation into the form that the product of two linear equations is equal to 0, and then make the two linear equations equal to 0 respectively, thus reducing the order. This solution is called factorization.

2. The main steps of factorization method to solve the quadratic equation of one variable:

(1) transforms the equation into the form that the right side is equal to 0;

(2) The left factor of the equation (the product of two linear factors) is decomposed into the form of (ax+m) (bx+n) = 0;

(3) Find the root of the equation from AX+M = 0 or BX+N = 0.

3. Comparison of direct opening method, collocation method, formula method and factorization method

X2 = a (a ≥ 0) or (ax+b) 2 = c (c ≥ 0) is solved by direct open method. Because the formula for finding the root of a quadratic equation with one variable is derived by collocation method, the root of a quadratic equation with one variable in general form is not required, so factorization or formula method can be considered.

1. For some equations, factorization is faster. Generally, factorization should be considered first in selecting methods, and other methods should be considered if factorization is not suitable.

2. Pay attention to the mathematical thinking method of experiencing analogy, transformation and reduction. The basic idea of solving a linear equation with one variable is to sort the unknown coefficients into1; The basic idea of solving a quadratic equation with one variable is to transform the quadratic equation with one variable into a quadratic equation with one variable by square root or factorization.