1. Understand the background of the topic: We need to understand the background and requirements of the topic. This includes given conditions, unknowns and targets.

2. Establish mathematical equations: According to the topic, we can establish one or more mathematical equations. These equations are based on the quantitative relationship and mathematical model in the topic.

3. Perform calculation: Use mathematical tools (such as paper and pencil, calculator or programming language) to solve equations. At this point, we may get one or more solutions.

4. Test the rationality of the solution: We need to consider the rationality of the solution. For example, if the solution is negative, but in practical problems, the solution should be non-negative, then the solution is wrong.

5. Back to the topic: bring the solution back to the topic to see if it meets the conditions and requirements of the topic. For example, if the problem requires solving an equation and finding the value of X, and the value of the solution of X is -5, then the solution can't meet the requirements of the problem, because X can't be negative.

6. Reconsideration: If the solution is unreasonable or can not meet the requirements of the topic, then it is necessary to reconsider the conditions of the topic, the establishment of the equation or the calculation method.

7. Record the results: Record the correct solution and inspection process for future reference.

Techniques for testing equations:

1, substitution method: substitute the solution of the equation into the original equation and check whether both sides of the equal sign are equal.

2. Simplification method: simplify the known equation, convert the complex equation into a simple equation, and check whether the simplified equation is equal to the original equation.

3. Comparison method: compare the coefficients and constant terms of the two equations to determine whether they are equal.

4. Estimation method: according to the range of coefficients in the equation, estimate the solution of the equation, and then substitute it into the original equation for testing.

5. Mirror image method: For some unary quadratic equations, you can draw the corresponding parabolic image to see if the intersection of the image and the X axis is the solution of the equation.

6. Root method: For some higher-order equations or unary complex quadratic equations, we can use the properties of roots to estimate the solutions of the equations and test them.

7. Variant method: according to whether the variant of the original equation is established, judge whether the solution of the original equation is correct.

8. Reduction to absurdity: Assuming that the solution of the original equation is incorrect, the contradiction is obtained through deduction, thus proving that the solution of the original equation is correct.