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elena-s [515]
2 years ago
8

Determine the next step for solving the quadratic equation by completing the square

Mathematics
1 answer:
GaryK [48]2 years ago
8 0

Answer:

  • The two solutions are:           x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}

  • The next and every step are below.

Explanation:

1. -3=-2x^2+2x    : Given (addition property / add - 3 to both sides)

2. -3 = - 2(x^2-x)    : Given (commom factor - 2)

3. -3-1/2=-2(x^2-x+1/4)

    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

5. Divide both sides by - 2 to get the next expression:

-7/4=(x-1/2)^2

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}

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Type the correct answer in each box
Luba_88 [7]

Answer:

We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.

We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :

1 - We first group terms with the same variable :

(x²+8x) + (y²+22y) + 37 = 0

2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)

(x²+8x) + (y²+22y) = - 37

3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.

x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²

y²+22y = (y²+22y+11²)-11² = (y+11)²-11²

4 - We plug the new values inside our equation :

(x+4)² - 4² + (y+22)² - 11² = -37

(x+4)² + (y+22)² = -37+4²+11²

(x+4)²+(y+22)² = 100

5 - We re-write in standard form :

(x-(-4)²)² + (y - (-22))² = 10²

And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)

5 0
3 years ago
What is 3.31 + 1 kilometer
MArishka [77]

Answer:

4.31 kilometer

..........................................

5 0
2 years ago
If Owen and Eliza had a combined taxable income of $68,200 and filed their federal income tax return with the Married Filing Joi
tangare [24]

Answer:

9425

D

Step-by-step explanation:

They are in the third tax bracket down. That means that their joint income is over 67900 but less than 137050.

The base rate is 9350. But they are 68200 - 67900 = 300  over the minimum.

So 25% of that 300 is also to be paid to the government 25/100 * 300 = 75 dollars

Now they must pay 9350 + 75 = 9425

Answer D


7 0
3 years ago
Read 2 more answers
If 3/15 is equivalent to 45/n. find n
Radda [10]

Answer:

n = 225

Step-by-step explanation:

Multiply 15 by 15

3 0
2 years ago
Read 2 more answers
In a certain computer, the probability of a memory failure is 0.01, while the probability of a hard disk failure is 0.02. If the
ratelena [41]

Answer:

We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:

P(A \cap B) = P(A) *P(B)

For this case we have that:

P(A) *P(B) = 0.01*0.02= 0.0002

And we see that 0.0002 \neq P(A \cap B)

So then we can conclude that the two events given are not independent and have a relationship or dependence.

Step-by-step explanation:

For this case we can define the following events:

A= In a certain computer a memory failure

B= In a certain computer a hard disk failure

We have the probability for the two events given on this case:

P(A) = 0.01 , P(B) = 0.02

We also know the probability that the memory and the hard drive fail simultaneously given by:

P(A \cap B) = 0.0014

And we want to check if the two events are independent.

We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:

P(A \cap B) = P(A) *P(B)

For this case we have that:

P(A) *P(B) = 0.01*0.02= 0.0002

And we see that 0.0002 \neq P(A \cap B)

So then we can conclude that the two events given are not independent and have a relationship or dependence.

8 0
2 years ago
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