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
bonufazy [111]
3 years ago
10

Solve each quadratic equation by completing the square. 6. x2 + 2x = 8 7. x2 - 6x = 16 8. x2 - 18x = 19 9. x2 + 3x = 3 10. x2 +

7x = 8
Mathematics
1 answer:
Andrei [34K]3 years ago
7 0
Lets get started :)

These questions have asked us to solve by completing the square.
How do we? I have attached a picture, which will explain

6. x² + 2x = 8
→ b is the coefficient of x, which is 2
→ We take half of 2 and square it. Then, we add it to either side

x² + 2x + (\frac{2}{2} )^2 = 8 + ( \frac{2}{2})^2
x² + 2x + 1 = 8 + 1
( x + 1 )( x + 1 ) = 9
( x + 1 )² = 9
\sqrt{( x + 1 )^2} = \sqrt{9}
x + 1 = + 3 or x + 1 = - 3
    x = 2     or     x = - 4

7. x² - 6x = 16

→ We do the same thing we did in the previous question

x² - 6x + (\frac{6}{2})^2 = 16 +  (\frac{6}{2})^2 
x² - 6x + 9 = 16 + 9
(x - 3)² = 25
\sqrt{(x-3)^2} =  \sqrt{25}
x - 3 = + 5 or x - 3 = - 5
   x = 8      or       x = - 2

8. x² - 18x = 19

x² - 18x + ( \frac{18}{2} )^2 = 19 + ( \frac{18}{2})^2
x² - 18x + 81 = 19 + 81
( x - 9 )( x - 9 ) = 100
( x - 9 )² = 100
\sqrt{(x-9)^2} =  \sqrt{100}
x - 9 = + 10 or x - 9 = -10
   x = 19      or      x = - 1

9. x² + 3x = 3

x² + 3x + ( \frac{3}{2} )^2 = 3 +  (\frac{3}{2} )
x^2 + 3x +  \frac{9}{4} = 3 +  \frac{9}{4}
x^{2} + 3x +  \frac{9}{4} =  \frac{21}{4}
(x^2 +  \frac{3}{2} ) ( x^2 +  \frac{3}{2} ) =  \frac{21}{4}
( x^2 + \frac{3}{2} )^2 =  \frac{21}{4}
\sqrt{ x^2 + \frac{3}{2} } =  \sqrt{ \frac{21}{4} } 
x +  \frac{3}{2} = + \frac{ \sqrt{21} }{2} or x +\frac{3}{2} = -  \frac{ \sqrt{21} }{2}
x = \frac{-3+ \sqrt{21} }{2} or x = \frac{-3 - \sqrt{21}}{2}


You might be interested in
4 batches of punch each batch has 16 fluid oz lemon juice and 4 pints of orange juice if each serving is 1 cup how many servings
Fudgin [204]

Answer:

40 servings.

Step-by-step explanation:

First we need to know the relation between pint and cup, and between oz and cup:

1 pint = 2 cup

8 oz = 1 cup

Now, we have that each batch has 16 fluid oz of lemon juice and 4 pints of orange juice, that is, 2 cups of lemon juice and 8 cups of orange juice, in a total of 10 cups.

If we have 4 batches, we have a total of 4 * 10 = 40 cups

So if each serving is 1 cup, the total made is equal to 40 servings.

6 0
3 years ago
Which expression is equivalent to 4/9 (2n - 3n)
yaroslaw [1]
I believe the answer is:
A. 8/9 n-11/3
6 0
3 years ago
Read 2 more answers
What’s the correct answer for this question?
pav-90 [236]

Answer: choice C

Step-by-step explanation:

The union of events A and B, denoted  ∪ , is the collection of all outcomes that are elements of one or the other of the sets A and B, or of both of them. It corresponds to combining descriptions of the two events using the word “or.”

**keep in mind that we don’t write numbers more than once in these sets(choiceB)

so the answer would be

{3,4,5,6,7,8,9}

5 0
3 years ago
Find the slope of the line that passes through (-3,-1) and (-5,4)
tester [92]

Line is Passing through the Points (-3 , -1) and (-5 , 4)

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

\heartsuit\;Slope(m) = \frac{y_1 - y_2}{x_1 - x_2}

here x₁ = -3 and x₂ = -5 and y₁ = -1 and y₂ = 4

\heartsuit\;Slope(m) = \frac{-1 - 4}{-3 + 5} = \frac{-5}{2}

3 0
3 years ago
Assignment 01.12 learning path one activity
hodyreva [135]
Why ask why?  ';lkl!!!!!!!!!!
8 0
3 years ago
Other questions:
  • You have 3,000 square feet of selling space. You want to reserve at least 80 square feet for each product category you
    13·1 answer
  • Smh I seriously don’t understand how I’m this freaking dumb
    6·2 answers
  • Doug has volunteered to help with the community clean-up project. He will work a total of 1779 hours. He plans to work 313 hours
    14·1 answer
  • Decimal
    9·1 answer
  • What is the slope of the line passing through (2,2) and (10,6)
    6·1 answer
  • Martin has 48 blue balloons and 36 orange balloons he separates the balloons into mixed groups of blue and orange there are the
    10·1 answer
  • You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is sign
    6·1 answer
  • Help with the questions below!
    15·1 answer
  • Congruent figure help please :)
    11·1 answer
  • 9 years 11 months =<br> _months?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!