Answer:
put a picture up
Step-by-step explanation:
Answer:
n = 9
Step-by-step explanation:
3(n+7)=48
distribute
3n +21 = 48
subtract 21 from each side
3n = 48-21
3n = 27
divide by 3
3n/3 = 27/3
n = 9
Answer: 3.64, 10.00
Step by step:
Answer:
![\frac{1}{2} x +x = 2 (x-4)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20x%20%2Bx%20%3D%202%20%28x-4%29)
Step-by-step explanation:
Suppose number is x
Following equation can be written from question statement
![\frac{1}{2} x +x = 2 (x-4)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20x%20%2Bx%20%3D%202%20%28x-4%29)
Simplifying it further
![\frac{3}{2} x = 2x-8](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%20x%20%3D%202x-8)
![\frac{3}{2} x -2x=-8](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%20x%20-2x%3D-8)
![\frac{3x-4x}{2}= -8](https://tex.z-dn.net/?f=%5Cfrac%7B3x-4x%7D%7B2%7D%3D%20-8)
![-x= -16\\x=16](https://tex.z-dn.net/?f=-x%3D%20-16%5C%5Cx%3D16)
Answer:
- The two solutions are:
![x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D%2B%2F-%5Cfrac%7B%5Csqrt%7B7%7D%20%7D%7B2%7D)
- The next and every step are below.
Explanation:
1.
: Given (addition property / add - 3 to both sides)
2.
: Given (commom factor - 2)
3. ![-3-1/2=-2(x^2-x+1/4)](https://tex.z-dn.net/?f=-3-1%2F2%3D-2%28x%5E2-x%2B1%2F4%29)
To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.
Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.
4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:
![-7/2=-2(x-1/2)^2](https://tex.z-dn.net/?f=-7%2F2%3D-2%28x-1%2F2%29%5E2)
5. Divide both sides by - 2 to get the next expression:
![-7/4=(x-1/2)^2](https://tex.z-dn.net/?f=-7%2F4%3D%28x-1%2F2%29%5E2)
6. The last step is to extract squere root from both sides of the equality:
![(x-1/2)=+/-\sqrt{\frac{7}{4}}\\ \\ x-1/2=+/-\frac{\sqrt{7} }{2}\\ \\ x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}](https://tex.z-dn.net/?f=%28x-1%2F2%29%3D%2B%2F-%5Csqrt%7B%5Cfrac%7B7%7D%7B4%7D%7D%5C%5C%20%5C%5C%20x-1%2F2%3D%2B%2F-%5Cfrac%7B%5Csqrt%7B7%7D%20%7D%7B2%7D%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B1%7D%7B2%7D%2B%2F-%5Cfrac%7B%5Csqrt%7B7%7D%20%7D%7B2%7D)