Matching Methods and Formulas Process and Answers

Formula Method. Needless to say.

direct simplification; You can also use (x+3) as.

variable s. Rule.

s=0 is obviously a general solution.

And. x=-3 both. Dividing.

s is simplified to.

2s=s-3

s=-3 x=0

Hence two answers.

Use the formula method.

If the multiplication formula is reversed, some polynomials can be factored, which is called the formula method.

Square Difference Formula: A2-B 2=(A+B)(A-B);

Perfect square formula: a2 2ab b 2 (a b) 2;

Note: A polynomial that can be factored using a perfectly squared formula must be trinomial, two of which can be written as the sum of the squares of two numbers (or equations) and the other as twice the product of the two numbers (or formulas).

Cube sum formula: a 3 + b 3 = (a + b) (a 2-ab + b 2);

Cubic deviation formula: a 3-b 3 = (a - b) (a 2 + ab + b 2);

The perfect cubic formula: a 3 a 2b 3ab 2 b 3 = (a b) 3

Please refer to ** above for the rest of the formulas.

For example: a 2

4ab+4b^2

a+2b)^2

For general quadratic function recipes, the others can be turned into general functions first and then recipes:

Let y=ax 2+bx+c(a≠0).

then y=a(x 2+bx a)+c

a(x^2+2bx/(2a)+(b/2a)^2)+c-b^2/(4a)

a(x+b/(2a))^2+(4ac-b^2)/(4a)

The formula for the formula in mathematics is to reduce the quadratic coefficient to 1, and then accompany the square of half of the coefficient of the primary term.

This method is to polynomialize the following forms to the coefficients a, b, c, d, and e in the above expression, which can also be expressions themselves, and can be combined with variables other than x. Here are some examples:

2x²+8x+5=2（x²+4x）+5

2（x²+4x+2²）+5-8

2（x+2）²-3

In a one-dimensional quadratic equation, the matching method is actually to shift the one-dimensional quadratic equation and add half of the square of the absolute value of the coefficient of the primary term on both sides of the equal sign.

Example – Solve the equation: voltaic bracelet 2x + 6x + 6 = 4

Solution: 2x +6x+6=4

(The square root of x+x+.)

x²-2x-8=0

x²-2x+1-1-8=0

x²-2x+1-9=0

x-1)²=9

x-1=±3

The solution is x1=4 x2=-2

Matching method One of the solutions in the mathematical one-dimensional quadratic equation (the other two are the formula method and the decomposition method) The specific process is as follows:

1.This unary quadratic equation is reduced to the form ax 2+bx+c=0 (this unary quadratic equation satisfies the real root).

2.The quadratic coefficient is reduced to 1

3.Move the constant term to the right of the equal sign.

4.The left and right sides of the equal sign are simultaneously added to the square of half of the coefficient of the primary term 5Write the algebraic formula to the left of the equal sign in perfectly squared form.

6.The left and right sides are squared at the same time.

7.Sorting out can get the root of the original equation.

Example: Solve the equation 2x 2+4=6x

: Add 3 and a half squared, and at the same time -2 also add 3 and a half squared to make both sides of the equation equal) 5( a 2+2b+1=0 i.e. (a+1) 2=0)x2=1

The matching method is based on the perfect square formula: (a+ -b) = a + 2ab+b.

The formula is only applicable to equations, that is, to add or subtract a number from the equation on the left and right sides at the same time, so that the formula on the left side of the equation becomes a completely flat formula, and then the equation can be solved by factoring.

Example: 2a -4a + 2 = 0

a -2a+1=0 (the coefficient of the quadratic term should be reduced to 1 first, which is convenient to solve the problem by the matching method, so both sides of the equation are divided by the coefficient of the quadratic term 2).

a-1) = 0 (the formula in the previous step found that the left side is perfectly square, so according to the perfect square formula, the factor a-2a+1 is factored into (a-1), so that the formula is completed).

a-1=0 (both sides of the final equation are squared at the same time).

a=1 (results obtained).