First, the main points of knowledge:

One-dimensional quadratic equation and one-dimensional linear equation are both integral equations, which are a key content of junior high school mathematics and the basis of studying mathematics in the future.

The foundation should attract students' attention.

The general form of the unary quadratic equation is: ax2+bx+c=0, (a≠0), which contains only one unknown, and the highest order of the unknown is 2.

The whole equation of.

The basic idea of solving quadratic equations with one variable is to simplify them into two quadratic equations with one variable. Quadratic equation with one variable has four solutions.

Methods: 1, direct Kaiping method; 2. Matching method; 3. Formula method; 4. Factorial decomposition method.

Second, detailed methods and examples:

1, direct Kaiping method:

The direct Kaiping method is a method to solve a quadratic equation with a direct square root. Solving (x-m)2=n (n≥0) by direct Kaiping method.

The solution is an equation of x = m.

Example 1. Solve the equation (1) (3x+1) 2 = 7 (2) 9x2-24x+16 =1.

Analysis: (1) This equation is obviously easy to do by direct flattening, (2) The left side of the equation is completely flat (3x-4)2, and the right side =11>; 0, so

This equation can also be solved by direct Kaiping method.

(1) solution: (3x+ 1)2=7×

∴(3x+ 1)2=5

∴ 3x+ 1 = (be careful not to lose the solution)

∴x=

The solution of the original equation is x 1=, x2=.