One-dimensional quadratic equation 1, direct Kaiping method; 2. Matching method; 3. Formula method; 4. Factorial decomposition method. Step-by-step solution and its application (suitable for junior high school mathematics) Solution of quadratic equation in one variable;

First, the direct Kaiping method

The form is (x+a) 2 = b, when b is greater than or equal to 0, x+a= plus or minus radical number b, x=-a plus or minus radical number b; When b is less than 0. This equation has no real root.

Second, the matching method

1. The quadratic term is converted to 1.

2. Shift the term, with quadratic term and linear term on the left and constant term on the right.

3. Formula, add half the square of the first-order coefficient on both sides and change it into the form of (x = a) 2 = b.

4. Solve the equation by direct Kaiping method.

Third, the formula method

Now the equation is arranged in a general form: ax 2+bx+c = 0. Then substitute abc into the formula x = (-b √ (b 2-4ac))/2a, and (b 2-4ac is greater than or equal to 0).

Fourthly, factorization method.

If the algebraic expression on the left of the unary quadratic equation AX 2+BX+C = 0 is easy to decompose, then the factorization method is preferred.

Extended data:

Generally speaking, the formula B 2-4ac is called the discriminant of the root of the unary quadratic equation AX 2+BX+C = 0, which is usually expressed by the Greek letter "δ", that is, δ = B 2-4ac.

1, when δ >; 0, the equation AX 2+BX+C = 0 (A ≠ 0) has two unequal real roots;

2. When δ = 0, the equation AX 2+BX+C = 0 (A ≠ 0) has two equal real roots;

3. When δ