Examples are as follows:
2x？ +8x+5=2(x？ +4x)+5
=2(x？ +4x+2？ )+5-8
=2(x+2)？ -3
Extended data:
Matching method refers to transforming a formula (including rational formula and transcendental formula) or a part of a formula into a completely flat way or the sum of several completely flat ways through continuous deformation. This method is called matching method. This method is often used in identity deformation, and it is one of the powerful means to solve the problem by discovering the hidden conditions in the topic.
In basic algebra, collocation method is a method for transforming quadratic polynomial into the sum of the square of linear polynomial and constant. This method converts the polynomial in the following form into the coefficients A, B, C, D and E in the above expression, which can also be expressions and contain variables other than X. Matching method is usually used to derive the root formula of quadratic equation: our purpose is to turn the left side of the equation into a complete square.
Because the perfect square in the question has (x+y)? = x？ + 2xy + y？ 2xy = (b/a)x, so y = b/2a. Add y =(b/2a) to both sides of the equation? , available:
This expression is called the root formula of quadratic equation.
When solving the equation, in the unary quadratic equation, the matching method is actually to shift the terms of the unary quadratic equation and add the square of half the absolute value of the coefficient of the first term on both sides of the equal sign.
Example solution equation: 2x? +6x+6=4
Analysis: the original equation can be arranged as: x? +3x+3=2, which can be obtained by the formula (x+ 1.5)? = 1.25 can be solved by finding the root.
Solution: 2x? +6x+6=4
& lt= & gt(x+ 1.5)？ = 1.25
X+1.5 = the square root of 65438 +0.25.
Baidu encyclopedia matching method