Application of quadratic equation of one variable in grade two of junior high school The cost price of a commodity is 200 yuan, which is 50% higher than the cost price. Due to poor sales, the price after two consecutive price cuts is 192 yuan. If the two price cuts are the same, calculate the price reduction rate

Let the percentage of price reduction be X,
The original price of clothes is: 200 (1 + 50%) = 300
The price after the first reduction is 300 (1-x),
The price after the second reduction is 300 (1-x) ^ 2;
Therefore, the countable equation: 300 (1-x) ^ 2 = 192
The solution is x = 0.2
So the price reduction rate is 20%
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In the first quarter of production, the output value of a factory in January is 2.5 million yuan, and the monthly growth rate of the output value in February and March is the same. It is known that the total output value in the first quarter is 8.436 million yuan, so the monthly growth rate of February and March is calculated

Suppose that the monthly growth rate of February and March is X. according to the meaning of the question, 250 + 250 (1 + x) + 250 (1 + x) 2 = 843.6250 + 250 + 250x + 250 + 500X + 250x2 = 843.6250x2 + 750x-93.6 = 0, (5x + 15.6) (50x-6) = 0, the solution is X1 = - 3.12 (negative value is not the meaning of the question, rounding off), X2 = 0.12 = 12%. Answer: the monthly growth rate of February and March is 12%

Today, the manager came to me and asked me to solve a quadratic equation with one variable. I couldn't solve it,
The original problem is: R ^ 2 + 3.1415r-38 = 0
I took one step: R ^ 2 + 3.1415r = 38,
-- please give me the detailed solution and reasons. I'm really ashamed to give everything back to the teacher,

It can be directly calculated by the root formula
r=[-3.1415±√(3.1415²+4×38)]/2
therefore
r= -7.9321378644915214759304296555859
Or r = 4.790637864491521475930429655859

When the value of a is what, the fraction: A & # 178; - 9 of a & # 178; + 6A + 9 is meaningless?

When a = 3 or a = - 3, the fraction: A & # 178; - 9 of a & # 178; + 6A + 9 is meaningless

2% x + 2 minus 3% 2x + 3 = 1,

3(x+2)-2(2x+3)=6
3x+6-4x-6=6
-x=6,
x=-6.

The number of equations and unknowns in high school equations
It's not university. Generally, several equations and several unknowns can be solved. Conic curve needs to see if it can be solved. For example, can high school students solve three equations and four unknowns
-c-x1=2.5x2
X1 + x2 = 6C (k Square) / (3K square + 2)
X1 * x2 = (3kc square - 6C Square) / (3K square + 2)
Can we solve the K value alone

Yes, it can be brought in as a whole and then calculated back. Generally, it can be done

Function f (x) = - 2x & # 178; + 6x (- 2 < x)

Two methods (1) draw the image, according to the image is easy to see the range
（2）y=-2(x-3/2)^2+9/2
By - 2

The absolute value of 15 out of 17 minus 15 out of 16 minus (15 out of 16 plus 2 out of 17)

It's - 1. I've done it with a smart calculator

（1）（a＋b）（a＋b－6）＋9 （2）x^2－9y^2＋x＋3y

（a＋b）（a＋b－6）＋9
=(a+b)^2-6(a+b)+9
=(a+b-3)^2
x^2－9y^2＋x＋3y
=(x-3y)(x+3y)+(x+3y)
=(x+3y)(x-3y+1)

If the square of X-9 = 0, what is the value of the square of x-3 / x-5x + 6
It is known that 5 / x = 3 / y, then the square of X + Y / x + X-Y / Y - (X-Y) (x + y) is
1 / a - 1 / B 1 / A + 1 / B is equal to

If the square of X-9 = 0, what is the value of the square of x-3 / x-5x + 6
(x + 3) (x-3) = 0, so x = 3 or x = - 3
（x²-5x+6）÷（x-3）
=（x-2）（x-3）÷（x-3）
When x = 3, it is meaningless
When x = - 3, it is equal to - 3-2 = - 5
It is known that 5 / x = 3 / y, then the square of X + Y / x + X-Y / Y - (X-Y) (x + y) is
1 / a - 1 / B 1 / A + 1 / B is equal to