2x 5x 3 0 Solve equations with the matching method?

[Cross multiplication.

2x²-5x-3=0Solution: (2x+1)(x-3)=0Yes, 2x+1=0, and x-3=0,solution, x= -1 2, and x=3;After testing, x=-1 2 and x=3 are the solutions of the original equations.

First, the quadratic term coefficient is removed, and both sides of the equation are divided by 2 at the same time to obtain:

x²-(5/2)x-(3/2)=0

Then make up the perfect square term (5 4) according to the coefficient of the primary term 5 2

x²-(5/2)x+(5/4)²-5/4)²-3/2)=0x-(5/4)]²49/16)=0

x-(5 4) = (49 16) = 7 4x = (5 4) (7 4) = 3 or -1 2

Because 2=1 2,-3=-3 1,-5=-3 2+1 1. Therefore, using the cross multiplication method, it can be decomposed into (2x+1)(x-3)=0, and the solution is x=-1 2 or x=3.

=2x 2-2x+6 =2(x-1 2) 2+11 2, when x=y=1 2, z takes the minimum value 11 2 2.? 3.

From the equation x 2-5x + 6 = 0 to get x1 = 2, x2 = 3 ∴y＂-5y'The general solution of +6=0 is y=c1e (2x)+c2e (3x), y -5y.

Solution: 2x Friends +3x-5=0

2x+5)(x-1) early hilarity = 0

The locust is pronounced with 2x+5=0 or x-1=0

x=-5 2 or x=1

You asked: Use the matching method to solve Fang Min's vertical Xicheng 2x -3x+5=0

Solution: Because =(3) -4 2 5=9-40=-31 0, the bridge of this equation is almost unsolved in the range of real numbers.

x²-2x-5/2=0

x -2x+1=5 Jinghuaisen 2+1

x-1)²=7/2

x-1)²=14/4

x-1 = 14 such as 2 or x-1=- 14 2, so x=1+ 14 2 or x=1- 14 2

2（x+5/4）^2=34/16

Then x+5 4 = 17 4

So x= 17 4-5 4

This kind of problem should be infiltrated into the lesion directly with the ruler dry formula.

Shifts the term from the original equation.

x 2 +5x=3, add half of the square of the coefficient of the primary term on both sides of the equation at the same time.

x 2 +5x+( 5 2 ) 2 =3+ 25 4 ，∴x+ 5 2 ) 2 = 37 4

x+ 5 2 =±37 2

solution, x= -5 37 2

x 1 = 5+ 37 2 ， x 2 = 5- 37 2 ．

After the recipe, you get:

2x²+3x-5=0

2(x²+3x/2)=5

2(x+3/4)²=5+9/8

x+3/4)²=49/16

x+3/4=±7/4

x = 1 or -5 2

About the solution of a quadratic equation:

1. Direct leveling method.

The method of finding the solution of a quadratic equation by directly opening the square using the definition of square root is called the direct square method.

According to the definition of square root, it can be seen that x+a is the square root of b, at that time, ; When b<0, the equation has no real roots.

To find the root of a quadratic equation by the direct open-level method, we must correctly use the property of the square root, that is, there are two square roots of positive numbers, which are opposite to each other, the square root of zero is zero, and negative numbers have no square root.

2. Matching method.

The matching method is an important mathematical method, which is not only used in solving one-dimensional quadratic equations, but also has a wide range of applications in other fields of mathematics.

The rationale for the matching method is a perfectly squared formula, and if a in the formula is regarded as an unknown number x and replaced by x, then there is .

3. Formula method.

The formula method is a method of solving the solution of a quadratic equation with a formula for finding the root, and it is a general method for solving a quadratic equation.

Formula for finding the root of a quadratic equation:

The root finding formula is specially used to solve a quadratic equation, so it first requires a≠0; Yes, because the number of squares must be non-negative, the second condition is b2-4ac 0. That is, the prerequisites for the root finding formula are a≠0 and b2-4ac 0.

4. Factorization.

The factorization method is a method of using the means of factorization to find the solution of the equation, which is simple and easy to do, and is the most commonly used method for solving a quadratic equation.

"Mathematics and Physics Q&A" answers for you, I hope it will be helpful to you.

2x²+3x-5=0

2(x²+3x/2)=5

2(x+3/4)²=5+9/8

x+3/4)²=49/16

x+3/4=±7/4

x = 1 or -5 2

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2x²+8x-3=0

x²+x²+4x+

x²+4x+4=4+

x+2)²=

x+2=±√

x= plus or minus 2, if simplified, you can also get plus or minus 22 minus 2).