How do you solve a quadratic equation?!?! Forget about 555

First, the equation is transformed into the following form by shifting the term – n 2 is the 2nd power of n, and n (1 2) is the square root of n.

an^2+bn+c=0

For your question is.

n^2+n-48=0

Then apply the formula for the solution of the second order equation.

n1=(-b+(b 2-4ac) (1 2)) 2an2=(-b-(b 2-4ac) (1 2)) After 2a is solved, it is good to discard the unreasonable solution according to the actual situation of the problem.

Move 48 to the right of the equal sign: n 2 + n - 48 = 0 and then use the discriminant b 2-4ac (according to ax 2 + bx + c = 0 (a>0).

Calculate their values again, and there are two.

x1,x2=[-b±√(b^2-4ac)]/2a

ax2+bx+c=0

Coefficients a, b, c

x1=(-b+sqr(b2-4ac)) 2ax2=(-b-sqr(b2-4ac)) 2asqr means open square.

If b2-4ac=0, then the equation has a unique solution.

1. Direct leveling method.

The direct leveling method is solved as (x-m) 2; The equation of =n (n 0), the solution of which is x= n+m

2. Matching method;

It is to synthesize the equation (x m) 2=n form, and then use the direct opening method, which is a very bloody solution, and generally does not use the equation to solve. However, it is very important when solving problems or two-dimensional images.

3. Formula method;

This method is the nemesis of all unary quadratic equations, and any unary quadratic equation can be solved by this method. The equation needs to be reduced to the form ax 2 + bx=c=0, when b -4ac 0, the equation has a solution, x = b [ b 4ac ] 2a

4. Factorization.

That is, the cross multiplication method, you need to have a very skilled observation ability of the number, when the right side of the equal sign is 0, for example, x 2-5x+6 = 0, the constant term is 6, which can be split into (-2) * (3) = 6, and the coefficient of the primary term is -5 = -2 + -3, so the equation can be synthesized (x-2) (x-3) = 0. This means that the sum of the two numbers multiplied by the constant term is equal to the coefficient of the primary term. For example, x 2 + 25 x + 100 = 0, the constant term is 100 = 20 * 5, and the coefficient of the primary term is 25 = 20 + 5, so the equation is combined to (x + 5) (x + 20) = 0.

Get a few more similar examples by yourself, and you will be familiar with them.

First of all, this is not a quadratic equation, but a quadratic inequality!

Solution: f'(x)=3(x^2)-6x-9

3[(x 2)-2x-3] (Factorization: Extracting the common factor 3) = 3(x+1)(x-3) (Factoring: Cross multiplication) 1, by f'(x) 0, there is:

x+1)(x-3) 0 i.e.: x+1 0, x-3 0.........1) Or: x+1 0, x-3 0.........2) By the group of inequalities (1), there are:

x -1, x 3, get: x 3 by the inequality group (2), have: x -1, x 3, get:

x -1 is combined to obtain: x 3, or: x -1;

2. By f'(x) 0, there is: (x+1)(x-3) 0 can be seen: x+1 and x-3 must have different signs, i.e.: x+1 and x-3 must be one positive and one negative).

Obviously: x-3 x+1

So: x+1 0, x-3 0

Solution: x -1, x 3

i.e.: -1 x 3.

Do you understand?

Let's say the price increases by $x.

600-10x）（40-30+x）=10000x=10

x = 40 in both cases.

The price is 40 + 10 = 50 yuan, and it should be 600-10 10 = 500 pieces, and the price is 40 + 40 = 80 yuan--- and it is rounded off.

Set a markup of x

10+x][600-10x]=10000 x=10 or 40 x=40 rounded so x=10 x+40=50 is given points

Generally, the price ...... is not directly setSet a price increase of x yuan first. (0 x 20) unit price - purchase price: 40-30+x

Number: 600-x

Profit = (Unit Price - Purchase Price) Number of units.

That is: (40-30+x) (600-x)=10000 and then just solve it yourself......

Move the right one to the left.

m²-3-5m-3=0

m²-5m-6=0

Factoring yields (m-6)(m+1)=0

m = 6 or -1

There are generally two ways to do this.

For example, solution x+y=8 1).

3x+y=12 2）

Method 1: Substitution equation method.

Obtained from (1).

y=8-x 3）

Replace (3) with (2).

3x+(8-x)=12

x=2 and then replace x=2 back to (1).

Get 2+y=8

y=6 Method 2: Addition and subtraction equation method.

2) Formula - (1) Formula.

Get 2x=4x=2 and substitute x=2 back to (1).

Get 2+y=8

y=6 In general, the first type is used.

15+15(1+x)+15(1+5x) 2=105 first divide by 15 to simplify, 1+(1+x)+(1+5x) 2=7 and then can only be honestly 25 x 2+11 x-4=0 formula x=(- 521-11) 50 or x=( 521-11) 50

Are you getting the equation wrong? Is it 15+15(1+x)+15(1+x) 2=105?

This one is easier to do.

15+15(1+x)+15(1+x)^2=1051+(1+x)+(1+x)^2-7=0

x^2+3 x-4=0

x-1) (x+4)=0

x=-4 or x=1

Since you haven't learned how to sum proportional sequences, that's the only way to do it.