The general steps to solve a quadratic equation with the fitting method are:

Match a quadratic equation into a <>

and then use the direct leveling method to solve the method.

1) Steps to solve a quadratic equation by the matching method:

Reducing the original equation to a general form;

Divide both sides of the equation by the quadratic coefficient to make the quadratic coefficient 1, and move the constant term to the right of the equation;

Add half of the square of the coefficient of the primary term to both sides of the equation;

The left side is matched into a perfectly flat method, and the right side is turned into a constant;

Further, the solution of the equation is obtained by the direct open-level method, and if the right side is a non-negative number, the equation has two real roots; If the right side is a negative number, then the equation has a pair of conjugate imaginary roots.

2) The theoretical basis of the matching method is the perfect square formula.

Example of a matching method for solving a quadratic equation:

1: Convert the coefficient of the second term to 1

3: Recipe you should know how to do it A represents the X square term, b represents the coefficient of the primary term, and c represents the constant term.

a+b 2) squared = c + 2 b ) squared.

4: Write the right side in the form of a root number.

5: Gives x1 x2

It's very simple, just look at the textbook.

1. Transform the original equation into a form;

2. Move the constant term to the right of the equation; The coefficient of the quadratic term is divided by the coefficient of the quadratic term on both sides of the equation at the same time, and the coefficient of the quadratic term is reduced to 1.

3. Add half of the square of the coefficient of the primary term on both sides of the equation at the same time;

4. Then make the left side of the equation into a completely flat method, and the right side into a constant;

5. If the right side of the equation is a non-negative number, then the two sides are directly squared to find the solution of the equation; If the right side is a negative number, then the equation has no real solution.

Reducing the original equation to a general form;

Divide both sides of the equation by the quadratic coefficient to make the quadratic coefficient 1, and move the constant term to the right of the equation;

Add half of the square coefficient on both sides of the square branch at the same time;

The left side is matched into a perfectly flat method, and the right side is turned into a constant;

Furthermore, the solution of the equation is obtained by the direct open-level method, and if the right side is a non-negative number, the equation has two real roots. If the right side is a negative number, then the equation has a pair of conjugate imaginary roots.

The fitting method solves the quadratic equation step1. Quadratic term coefficient: 1.

2. Shift term: Move the constant term c of the equation x2+bx+c=0 to the other side of the equation to obtain the equation x2+bx=-c.

4. Opening: Both sides of the equation are squared at the same time, the purpose is to reduce the order and obtain a one-dimensional equation.

5. The unary equation must be solved to obtain the solution of the original equation.

Precautions for solving one-dimensional quadratic equations by the matching method:1. The first step of the formula is best written in a square form, which can reduce the error rate of the second step of the formula.

2. It is recommended for beginners to write the penultimate step to reduce the error rate.

3. The last sentence cannot be changed to the original equation without solution, because it is only in the range of real numbers that there is no solution, and it has a solution after learning imaginary numbers in high school.

4. Observe before moving the item, if it can be matched into a perfect square, there is no need to move the item.

To solve a quadratic equation by the matching method, it is necessary to pay attention to first reducing the quadratic term coefficient of the unary quadratic equation to 1, and then adding half of the square of the previous quadratic term coefficient on both sides of the equation. The rationale for the matching method is the perfect square formula a + b + 2ab = (a + b).

Steps: Transform the original equation into a general form; Both sides of the equation are divided by the quadratic coefficient, so that the quadratic term coefficient is 1, and the number term of Changxiao hail is moved to the right side of the equation. Add half of the square of the coefficient of the primary term to both sides of the equation; The left side is matched into a perfectly flat method, and the right side is turned into a constant; Further, the solution of the equation is obtained by the direct open-level method, and if the right side is a non-negative number, the equation has two real roots; If the right side is a negative number, then the equation has a pair of conjugate imaginary roots.