General steps of solving a quadratic equation with one variable by collocation method;

1, the form of the original equation;

2. Move the constant term to the right of the equation; Both sides of the equation are divided by the coefficient of quadratic term at the same time, and the coefficient of quadratic term is converted into1;

3. Add the square of half the coefficient of the first term to both sides of the equation;

4. Match the left side of the equation into a completely flat way, and the right side becomes a constant;

5. If the right side of the equation is non-negative, square both sides directly to find the solution of the equation; If the right side is negative, it is judged that this equation has no real solution.

Extended data:

Matching method is usually used to derive the root formula of quadratic equation: our aim is to turn the left side of the equation into a complete square. Because the complete square in the question has (x? +? y)=？ x？ + 2xy？ +? In the form of y, we can deduce 2xy? = (b/a)x, so y? =? B/2a. Add y to both sides of the equation = (b/2a).

Example decomposition factor: x? -4x- 12

Solution: x? -4x- 12=x？ -4x+4-4- 12

=(x-2)？ - 16

=(x -6)(x+2)

Find the vertex coordinates of parabola

Find parabola y=3x? Vertex coordinates of +6x-3.

Solution: y=3(x? +2x- 1)=3(x？ +2x+ 1- 1- 1)= 3(x+ 1)？ -6

So the vertex coordinates of this parabola are (-1, -6).

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