1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
beks73 [17]
3 years ago
11

Solve x2 + 14x = −24 by completing the square.

Mathematics
2 answers:
Artyom0805 [142]3 years ago
7 0

Answer:

A. -12, -2

Step-by-step explanation:

Just took an Edge quiz.

Aleks04 [339]3 years ago
6 0

Option A

The solution set of the equation is {-12, -2}

<h3><u>Solution:</u></h3>

Given equation is:

x^2 + 14x = -24

We have to find the solution set of this equation by completing the square

First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x + 24 = 0 ----- eqn 1

<em><u>The general form of quadratic equation is:</u></em>

ax^2 + bx + c = 0 where a \neq 0

On comparing the given eqn 1 with general quadratic equation, we get

a = 1

b = 14

c = 24

In completing the square, we take half of coefficient of middle term "x" and then square it. Then we add it on both sides of the equation

So to complete the square, add (\frac{b}{2})^2 to both sides of the equation

x^2 + 14x + 24 + (\frac{14}{2})^2 = (\frac{14}{2})^2

x^2 + 14x + 24 + 7^2 = 7^2\\\\x^2 + 14x + 24 + 49 = 49

x^2 + 14x + 24 + 49 = 49\\\\x^2 + 14x + 49 = 49 - 24\\\\x^2 + 14x + 49 = 25\\\\(x + 7)(x + 7) = 25\\\\(x + 7)^2 = 25

Take square root on both sides

x + 7 = \sqrt{25}

x+7=\pm 5

Now make two equations

x + 7 = + 5 and x + 7 = -5

x = +5 - 7 = -2

x = -2

And,

x + 7 = -5

x = -5 - 7 = -12

x = -12

Therefore, the solution set of the equation is {-12, -2} and option A is correct

You might be interested in
Torrey has $20 to buy a birthday present for her that she does this to buy a CD for $18 the sales tax is 7% does she have enough
Effectus [21]
No, because she will go over by .57 cents. So she won't be able to buy the gift. You can find the answer by dividing 18 by 7 and adding that answer to 18 to get the amount total you owe including tax. 
8 0
3 years ago
Solve for x: 6x + 1 over 4 (4x + 8) &gt; 12
sukhopar [10]

Answer:

A. x>\frac{10}{7}.

Step-by-step explanation:

We have been given an inequality 6x+\frac{1}{4}(4x+8)>12. We are asked to solve the given inequality for x.

Using distributive property, we will get:

6x+\frac{1}{4}*4x+\frac{1}{4}*8>12

6x+x+2>12

7x+2>12

Subtract 2 from both sides:

7x+2-2>12-2

7x>10

Divide both sides by 7:

\frac{7x}{7}>\frac{10}{7}

x>\frac{10}{7}

Therefore, option A is the correct choice.

3 0
2 years ago
Two fewer than a number doubled is the same as the number decreased by 38. Find the number.
djyliett [7]
<span>2n - 2 = n - 38

hope it helps</span>
7 0
2 years ago
Read 2 more answers
in a standard casino dice game the roller wins on the first roll if he rolls a sum of 7 or 11. what is the probability of winnin
Alborosie

<u>Answer-</u>

<em>The probability of winning on the first roll is </em><em>0.22</em>

<u>Solution-</u>

As in the game of casino, two dice are rolled simultaneously.

So the sample space would be,

|S|=6^2=36

Let E be the event such that the sum of two numbers are 7, so

E = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

|E|=56

\therefore P(E)=\dfrac{|E|}{|S|}=\dfrac{6}{36}

Let F be the event such that the sum of two numbers are 11, so

F = {(6,5), (5,6)}

|F|=2

\therefore P(F)=\dfrac{|F|}{|S|}=\dfrac{2}{36}

Now,

P(\text{sum is 7 or 11)}=P(E\ \cup\ F)=P(E)+P(F)=\dfrac{6}{36}+\dfrac{2}{36}=\dfrac{8}{36}=\dfrac{2}{9}=0.22

8 0
3 years ago
Is the fraction 14/42 equal to 6/2
PilotLPTM [1.2K]

Answer:

No

Step-by-step explanation:

6/2=3

14/42=1/3=0.33333333333333333333

5 0
3 years ago
Read 2 more answers
Other questions:
  • Amantha wants to use her savings of $1140 to buy shoes and scarves. The total price of the scarves she bought was $80. Each pair
    10·2 answers
  • The regular price of an item is $84. The item is on sale witha discount of $12. What is the discount rate.
    8·1 answer
  • Tamara spun the arrow on a spinner 50 times. The number of times the arrow landed on each colored section of the spinner is show
    10·1 answer
  • The temperature changed from 7°F at 6 p.M to -5°F at midnight. What was the difference between the high and low temperatures? Wh
    11·1 answer
  • The sum of a whole number and twice the square of the number is 10. Find the number.
    11·1 answer
  • Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2 3 of the way there.
    13·1 answer
  • A large pizza has 16 slices. You eat 4 pieces and 7 chicken wings. What proportion of the pizza did you eat?
    15·1 answer
  • The measure of angle A is 68°. The measure of angle B is 22°. Which statement best describes the relationship between these two
    6·1 answer
  • What is the area of a triangle with a<br> base of 6m and a height of 7m
    15·1 answer
  • Help pls ! I’ll mark brainliest!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!