Shape (X-m)? The quadratic equation with one variable =n (n≥0) can be directly solved as x = m √ n by Kaiping method.
The left side of the equal sign is the square of a number, and the right side of the equal sign is a constant.
② The essence of order reduction is to transform a quadratic equation with one variable into two linear equations with one variable.
The method is to remove the square root according to the meaning of the square root.
(2) Matching method
Steps of solving a quadratic equation with one variable by collocation method;
① Turn the original equation into a general form.
② Divide both sides of the equation by the quadratic term coefficient, so that the quadratic term coefficient is 1, and move the constant term to the right of the equation.
③ Add the square of half the coefficient of the first term on both sides of the equation.
④ Make the left side completely flat and the right side constant.
⑤ Further use the direct Kaiping method to find the solution of the equation. If the right side is nonnegative, the equation has two real roots. If the right side is negative, then the equation has a pair of imaginary roots of yoke.
(3) Factor decomposition method
It is a method to solve the equation by factorization, and it is the most commonly used method to solve the quadratic equation of one variable.
Steps of factorization:
① Move the term and change the right side of the equation to (0).
② The left side is factorized into the product of two (first) factors.
(3) Make each factor equal to zero, and get (one-dimensional linear equations).
(4) Solve these two (one-dimensional linear equations) separately to get the solution of the equations.
(4) Root formula method
The general steps of solving a quadratic equation with one variable by finding the root formula are as follows:
(1) equation into the general form of aX? +bX+c=0, determine the values of a, b and c (note the symbols).
② Find the discriminant △=b? The value of -4ac, judge the situation of the root.
If △
related notion
1. An equation with an unknown number is called an equation, or an equation with an unknown number is an equation.
2. Holding the value of the unknown quantity of the equation is called the solution of the equation, or the root of the equation.
3. Solving the equation is the process of finding the values of all the unknowns in the equation.
4. The equation must be an equation, and the equation is not necessarily an equation. An equation without unknowns is not an equation.
5. Verification: After solving the equation, verification is needed. Verification is to substitute the unknown value into the original equation to see if both sides of the equation are equal. If they are equal, then the value obtained is the solution of the equation.
6. Note: Write the word "Xie", align the equal sign and check.
7. The equation depends on the relationship between the parts of the equation, and the relationship between addition, subtraction, multiplication and division (addend+addend = sum, and-where one addend = another addend, difference+subtraction = minuend, minuend-difference = subtraction, factor × factor = product, product/factor = another.