Solution of quadratic equation of one variable

Solution of quadratic equation of one variable

General solution
1. Preparation method
(all quadratic equations of one variable can be solved)
For example, to solve the equation: x ^ 2 + 2x-3 = 0
Move the constant term to x ^ 2 + 2x = 3
Add 1 to both sides of the equation (to form a complete square) to get x ^ 2 + 2x + 1 = 4
The factorization is: (x + 1) ^ 2 = 4
The solution is: X1 = - 3, X2 = 1
A pithy formula for solving quadratic equation of one variable with collocation method
The quadratic coefficient is reduced to one
Let's move the constant to the right
First order coefficient half square
On both sides add the most equivalent
2. Formula method
(all quadratic equations of one variable can be solved)
First of all, we should judge how many roots there are in the quadratic equation of one variable by the discriminant of the roots of Δ = B ^ 2-4ac
1. When Δ = B ^ 2-4ac0, X has two different real roots
When the judgment is completed, if the equation has roots, it can be divided into two cases: 2 and 3, then the equation has roots according to the formula: x = {- B ± √ (b ^ 2-4ac)} / 2A
To find the root of the equation
3. Factorization
(solvable partial quadratic equation of one variable) (factorization method is divided into "common factor method", "formula method" (divided into "square difference formula" and "complete square formula)" and "cross multiplication"
For example: solve the equation: x ^ 2 + 2x + 1 = 0
Using the factorization of the complete square formula, we get: (x + 1) ^ 2 = 0
The solution is: X1 = x2 = - 1
4. Direct leveling method
(solvable partial quadratic equation with one variable)
5. Algebraic method
(all quadratic equations of one variable can be solved)
　　ax^2+bx+c=0
At the same time divided by a, it can be changed to x ^ 2 + BX / A + C / a = 0
Let x = y-b / 2
The equation becomes: (y ^ 2 + B ^ 2 / 4-by) + (by + B ^ 2 / 2) + C = 0 x wrong__ It should be (y ^ 2 + B ^ 2 / 4-by) divided by (by-b ^ 2 / 2) + C = 0
Then it becomes: y ^ 2 + (b ^ 22 * 3) / 4 + C = 0 X___ y^2-b^2/4+c=0
　　y=±√[(b^2*3)/4+c] X ____ y=±√[(b^2)/4+c]

On the solution of quadratic equation of one variable
Please list all kinds of solutions to quadratic equation of one variable, late at night, afraid no one will answer, so there is no score, if there is a good one, you must score!

One variable quadratic equation solution 1. Knowledge points: one variable quadratic equation and one variable linear equation are integral equations, it is a key content of junior high school mathematics, and also the basis of learning mathematics in the future. The general form of one variable quadratic equation is ax ^ 2 (2 is the degree, that is, the square of x) + BX + C = 0, (a ≠ 0), it

Solution of quadratic equation of one variable
You teach me, I want examples, now do not give points, if the answer is good,

ax²+bx+c=0（a≠0）x²+（b/a）x+c/a=0,x²+（b/a）x+（b/2a）²-（b/2a）²+c/a=0,（x+b/2a）²-b²/4a²+c/a=0,（x+b/2a）²-（b²-4ac）/4a²=0,（x+b/2a）²=...