X ^ 2 + 4x + 8 = 2x + 11 and formula solution. How to solve

X ^ 2 + 4x + 8 = 2x + 11 and formula solution. How to solve

First, the original equation is transformed into one side equal to 0,
That is, x ^ 2 + 2x-3 = 0
① Using the formula X1 = [- B + radical (B & # 178; - 4ac)] / 2a, X2 = [- B - radical (B & # 178; - 4ac)] / 2a,
(a is the coefficient of quadratic term, B is the coefficient of primary term, C is the constant term)
Then, by substituting a = 1, B = 2, C = - 3, we can get x1, x2
② Because this equation is special, it can be decomposed by cross multiplication,
That is, (x-1) (x + 3) = 0,
We get X1 = 1, X2 = - 3
(ask again if you don't know)
Equal to the square of x plus 2x minus 3 equals 0
(x + 3) (x-1) is equal to 0
Let (2xa + 2) be a constant, where K + 2 is a constant
A. 2（x+1）2-3B. 2（x+1）2-2C. 2（x+2）2-5D. 2（x+2）2-9
Let y = 2x2 + 4x-1, according to the properties of quadratic function, the vertex coordinates of this quadratic function are x = - 42 × 2 = - 1, y = 4 × 2 × (− 1) − 164 × 2 = - 3, so the quadratic function y = 2x2 + 4x-1 can be changed into y = 2 (x + 1) 2-3
2/3x+3/4y=1/2 4/5x+5/6y=7/15 x= y=
2 / 3x + 3 / 4Y = 1 / 2 (1) 4 / 5x + 5 / 6y = 7 / 15 (2) 8x + 9y = 6 (2) 24x + 25y = 14 (3) 24x + 27y = 18 (5) - 4 2Y = 4 y = 2 (3) 8x + 18 = 6 x = - 3 / 2
The selling price of down quilt and summer cool quilt in a textile wholesale market is 415 yuan and 150 yuan respectively. A merchant bought 80 pieces of these two kinds of goods, and the total payment is no more than 20000 yuan. How many down quilts did the merchant buy at most?
2. Xiaoliang has 60 coins of 0.1 yuan and 0.5 yuan in his piggy bank. The total value is less than 20 yuan. How many coins of 0.5 yuan does he have at most?
3. Given the lengths of three sides of triangle are a, a + 1, a + 3, judge the value range of A
4 has a two digit number greater than 63. The sum of its one digit number and ten digit number is 9. What are the possible two digit numbers?
Several students of grade 5 and 8 took a group photo. It is known that the price of developing a negative is 0.35 yuan. We discussed that each student should get a photo, but everyone should share a negative. In this way, the average share of each student is less than 0.5 yuan. How many people participate in the group photo?
A at most 6. B at least 6. C at most 5. D at least 5
I'm sorry I got the wrong number for question 5
It should be: several students of Grade 8 took a group photo. It is known that the price of developing a negative is 0.8 yuan, and the price of developing a photo is 0.35 yuan. We agreed to share one photo. In this way, the average amount of money shared by each person is less than 0.5 yuan, and the number of students participating in the group photo () ABCD option remains unchanged
Let's suppose that we have bought x quilts 415x + 150 (80-x) ≤ 20000265x ≤ 8000x, and the maximum value is 30. Therefore, we have bought up to 30 quilts 2, X coins of 0.5 yuan, 0.5x + 0.1 (60-x) ≤ 200.4x ≤ 14x ≤ 35, so there are up to 35 coins of 0.5 yuan, 3, a + A + 1 > A + 3A > 24
There are so many questions on this topic that I've spent% >_
Find the nearest distance from point (0. A) to curve X ^ 2 = 4Y
Let the point on the curve be (x, x ^ 2 / 4), then the square of the distance from the point (0, a) to the point on the curve is d ^ 2 = f (x) = (x-0) ^ 2 + (x ^ 2 / 4-A) ^ 2 = x ^ 2 + x ^ 4 / 16-ax ^ 2 / 2 + A ^ 2 = x ^ 4 / 16 + (1-A / 2) x ^ 2 + A ^ 2 = 1 / 16 [x ^ 4 + 16 (1-A / 2) x ^ 2 + (8 (1-A / 2)) ^ 2] - 1 / 16 * (8 (1-A / 2)) ^ 2 + A ^ 2 = 1 / 16 [x ^ 2 + 8 (1
Inequality of degree one variable
1. Solve the following inequality:
(1) 3 x + 5 ＞ 1 + 5 x ； (2) 2 － 5 x ≥ 7－ 6 x ；
(3) x －3 / 2 ＞ x + 6 / 5 ； (3) 5 ( x + 2 ) / 4 ＞ 2 x －2.
2. Solve the following inequality:
(1) 1 0 － 4 ( x －3 ) ≤ 2 ( x －1 ) ； (2) x ＋5 / 2 － 1 ＜ 3 x + 2 / 2 .
3. Find the positive integer solution of inequality 3 (x-3) > 5x-9
4. The sum of a two digit number plus half of it is less than 20
5. A store bought 100 e-bikes at the purchase price of 2000 yuan each, and sold them at the price of 2600 yuan each. Two months later, the sales amount of e-bikes has exceeded the purchase price of these e-bikes. At this time, at least how many e-bikes have been sold?
6. If 40 sets of children's clothing are purchased at the price of 90 yuan per set in the clothing market, the tax payable is 10% of the sales. If you want to obtain a net profit of not less than 900 yuan, how much is the selling price of each set of children's clothing at least?
1.(1)x=900
x>=197.5
Find the longest and shortest distance from the point on the curve X ^ 3 + y ^ 3-xy = 1 (x > = 0, Y > = 0) to the origin
Restriction condition: x ^ 3 + y ^ 3-xy-1 = 0, X & gt; = 0, Y & gt; = 0 objective function: x ^ 2 + y ^ 2 Let f (x, y) = x ^ 2 + y ^ 2 + k * (x ^ 3 + y ^ 3-xy-1) DF / DX = 0df / dy = 0df / DK = 0 (D is partial derivative) get 2x + 3K * x ^ 2-k * y = 02y + 3K * y ^ 2-k * x = 0x ^ 3 + y ^ 3-xy-1 = 0 by Lagrange multiplier method, the solution is good
Solving inequality x (x-1) &# 178; (x + 1) &# 179; (x + 2) ≥ 0
There is a graph called odd through even not through. When x (x-1) (x + 1) (x + 2) is greater than or less than 0, the change of the positive and negative of the global polynomial is discussed respectively. The answer is as follows: when x ≤ - 2,
When - 2 ≤ x ≤ - 1
When - 1 ≤ x ≤ 0
When 0 ≤ x ≤ 1
X>1
Discuss separately
X ∈ [- 3, - 2] u [0, + infinity)
Analysis first = 0 point
Obviously x = 0,1, - 1, - 2
In the analysis > 0
At this point, we completely square them because they are always greater than zero
Therefore, X (x + 1) (x + 2) > 0
From the root of the number axis (- 2, - 1) (0, + infinity)
To sum up, X ∈ [- 2, - 1] ∪ [0, + infinity]
When x ≤ - 2,
When - 2 ≤ x ≤ - 1
When - 1 ≤ x ≤ 0
When 0 ≤ x ≤ 1
X>1
Discuss separately
If the line ax + 2BY-2 = 0 (a > 0, b > 0) always bisects the circumference of the circle x2 + y2-4x-2y-8 = 0, then the minimum value of 1A + 2b is ()
A. 1B. 3+22C. 5D. 42
According to the meaning of the title, a straight line passes through the center of the circle (2,1), so a + B = 1. 1A + 2B = (a + b) (1a + 2b) = 3 + Ba + 2Ab ≥ 3 + 22, if and only if Ba = 2Ab, the equal sign holds, so B is chosen
Solve the following inequality (2) x & # 178; - (a + A & # 178;) x + A & # 179; > 0
x²-(a+a²)x+a³>0
（x-a）(x-a²)>0
When a ≥ 1
x> A & # or X