Answer:
1. (x - 3)² = 8
2. (x + 2)² = 3
3. (x + 6)² = 
4. (x + 3)² = 27
5. (x + 4)² = 13
6. 
Step-by-step explanation:
Completion of Square: 
In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.
1. x² - 6x + 1 = 0
Taking the constant term to the other side, we get:
x² - 6x = - 1
⇒ x² - 2(3)x = -1
⇒ x² -2(3)x + 9 = - 1 + 9 [Adding 9 to both the sides]
⇒ x² -2(3)x + 3² = 8
⇒ (x - 3)² = 8 is the answer.
2. 3x² + 12x + 3 = 0
Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.
3x² + 12x = -3
Dividing by 3 through out, x² + 4x = - 1
⇒ x² + 2(2) + 4 = -1 + 4
⇒ x² +2(2) + 2² = 3
⇒ (x + 2)² = 3 is the answer.
3. 2x² + 24x = 29
x² + 12x = 
⇒ x² + 2(6)x + 36 =
+ 36
⇒ x² + 2(6)x + 6² = 
⇒ (x + 6)² =
is the answer.
4. x² + 6x - 18 = 0
x² + 6x = 18
⇒ x² + 2(3)x = 18
⇒ x² + 2(3)x + 9 = 18 + 9
⇒ x² + 2(3)x + 3² = 27
⇒ (x + 3)² = 27 is the answer.
5. x² + 8x + 3 = 0
x² + 8x = -3
⇒ x² + 2(4)x = -3
⇒ x² + 2(4)x + 16 = - 3 + 16
⇒ x² + 2(4)x + 16 = 13
⇒ (x + 4)² = 13 is the answer.
6. 9x² - 30x + 6 = 0
9x² - 30x = - 6
⇒ x²
x = - 6


is the answer.
I believe the equation is
![4 \sqrt[4]{2x} + 6 \sqrt[4]{2x}](https://tex.z-dn.net/?f=4%20%5Csqrt%5B4%5D%7B2x%7D%20%2B%206%20%20%5Csqrt%5B4%5D%7B2x%7D%20)
In this case, you would simplify it by adding them together.
![4 \sqrt[4]{2x} + 6 \sqrt[4]{2x}](https://tex.z-dn.net/?f=4%20%5Csqrt%5B4%5D%7B2x%7D%20%2B%206%20%20%5Csqrt%5B4%5D%7B2x%7D%20)
=
![10 \sqrt[4]{2x}](https://tex.z-dn.net/?f=10%20%20%5Csqrt%5B4%5D%7B2x%7D%20)
And can even be changed to an exponential equation:
Answer:
x=3
y=-2
Step-by-step explanation:
2x - 5y = 16
3x + 2y = 5
Solve for x in the first equation.
2x - 5y = 16
2x = 16 + 5y
x = (16 + 5y)/2
x = 8 + 5/2y
Put x as 8 + 5/2y in the second equation and solve for y.
3(8+5/2y) + 2y = 5
24+15/2y + 2y = 5
24 + 19/2y = 5
19/2y = 5-24
19/2y = -19
y = -2
Put y as -2 in the first equation and solve for x.
2x - 5(-2) = 16
2x +10 = 16
2x = 16-10
2x = 6
x = 3
Collect like terms
3g+11g-9-21
Add the like terms up
14g-30
if u have to simplify further, u have
2(7g-15)
Answer:
140,620,000
Step-by-step explanation:
There are two types of standard form. The one above (given to you) is the normal standard form. However, there is another one. This one would look like:
140,620,000 = 1.4062 x 10^8
Remember that in this standard form, you must move the decimal to just after the first place value, and the amount of moves you made for the decimal is the amount in the power over 10.
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