All categories

3 years ago

Solve the equation by completing the square. ^x2- 12x = -28

Mathematics

2 answers:

vova2212 [387]3 years ago

5 0

Answer:

x = 6 + 2√2 and x = 6 - 2√2

Step-by-step explanation:

Please write the " ^ " symbol between x and 2 here: x^2 - 12x = -28.

Take half the coefficient of x; here that is -6.

Square this, obtaining 36.

Add 36 to, and then subtract 36 from, x^2 - 12x: x^2 - 12x + 36 - 36.

Rewrite x^2 - 12x + 36 as the square of a binomial: (x - 6)^2.

Then rewrite x^2 - 12x = -28 as (x - 6)^2 - 36 = -28.

Simplifying, (x - 6)^2 = 8.

Taking the square root of both sides, x - 6 = plus or minus 2√2.

Then the solutions are x = 6 + 2√2 and x = 6 - 2√2

Olegator [25]3 years ago

3 0

x^2 -12 x = -28

(-12/2) ^ 2 =36

x^2 -12 x + 36 = -28 + 36

x^2 -12x + 36 = 8

(x-6)^2 = 8

take the square root of each side

x-6 = sqrt (8) x-6 = -sqrt (8)

you get a positive and a negative when taking the square root

x= 6 + sqrt (8)

x = 6 - sqrt (8)

sqrt (8) = 2 sqrt (2)

x= 6 + 2 sqrt (2)

x = 6 - 2 sqrt (2)

Answer:

x= 6 + 2 sqrt (2)

x = 6 - 2 sqrt (2)

You might be interested in

FREEEEEEE POIIIIIIIIINTS!!!!!!!!!!!!!!!!!!!!!!!!!

Travka [436]

Answer: thank you

Step-by-step explanation: have a good day :)

7 0

3 years ago

Read 2 more answers

What are the coordinates of the circumcenter of this triangle?

Oduvanchick [21]

Answer:

The coordinates of the circumcenter of this triangle are (3,2)

Step-by-step explanation:

we know that

The circumcenter is the point where the perpendicular bisectors of a triangle intersect

we have the coordinates

$A(-2,5),B(-2,-1),C(8,-1)$

step 1

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M=(\frac{-2-2}{2},\frac{5-1}{2})$

$M_A_B=(-2,2)$

step 2

Find the equation of the line perpendicular to the segment AB that passes through the point (-2,2)

Is a horizontal line (parallel to the x-axis)

$y=2$ -----> equation A

step 3

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M=(\frac{-2+8}{2},\frac{-1-1}{2})$

$M_B_C=(3,-1)$

step 4

Find the equation of the line perpendicular to the segment BC that passes through the point (3,-1)

Is a vertical line (parallel to the y-axis)

$x=3$ -----> equation B

step 5

Find the circumcenter

The circumcenter is the intersection point between the equation A and equation B

$y=2$ -----> equation A

$x=3$ -----> equation B

The intersection point is (3,2)

therefore

The coordinates of the circumcenter of this triangle are (3,2)

3 0

3 years ago

Which of the pairs of events below is mutually exclusive?

Nady [450]

Answer:

Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

Step-by-step explanation:

Given four pair of events:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards

To find:

Which of the pairs is mutually exclusive?

Solution:

First of all, let us have a look at the definition of mutually exclusive events.

Mutually exclusive events do not have any case in common.

In other words, two events are known as mutually exclusive when both the events can not occur at the same time.

Now, let us have a look at the given options one by one:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

We know that there is only one ace of spades in a standard deck.

Therefore, the two events can not occur one after the other, so these are mutually exclusive events.

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards.

The two events can occur one after the other, so these are not mutually exclusive.

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

3 0

3 years ago

Solve

grin007 [14]

Answer would be a (-1, ten-thirds) :)

8 0

3 years ago

I have no idea what this is-

Studentka2010 [4]

Answer:

the question is asking you to find the area i.e length of the angle and for that you have to find out the length of the xy and kz by making equations.

you can do Xy=Kz as they are parallel lines and i think the answer will be 5m and after finding the length do the following process

6 0

2 years ago

Read 2 more answers