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
What does the B mean in 1.9+b=3.2
Flura [38]
1.3
You subtract 3.2 from 1.9 ; which gives you 1.3
7 0
2 years ago
How can I get the anserw of 6.3 divided 0.7
gayaneshka [121]
You can use your calculator if you have one or do long division. just make sure to move the decimal so it looks like this: 63 divided by 7. you answer should be 9
6 0
3 years ago
Read 2 more answers
Determine if each graph represent a direct proportional or not
Troyanec [42]

Answer:

i hope everyone has a good day keep your head up at all times and dont give up

Step-by-step explanation:

5 0
3 years ago
A set of buttons sells for $2.75 and costs $0.55 to make. Twenty percent of the profit (the difference between the purchase pric
Rufina [12.5K]

Answer: b

Step-by-step explanation: I am 95% sure

6 0
2 years ago
Which expression is the simplest form of -(4x + y)n + 2(x - 3y)
Marina86 [1]

Answer:

\boxed{\bold{-4nx-ny+2x-6y}}

Explanation:

Rewrite:

= \bold{-n\left(4x+y\right)+2\left(x-3y\right)}

Expand \bold{-n\left(4x+y\right): \ -4nx-ny}

= \bold{-4nx-ny+2\left(x-3y\right)}

Expand \bold{2\left(x-3y\right): \ 2x-6y}

= \bold{-4nx-ny+2x-6y}

Mordancy.

4 0
3 years ago
Other questions:
  • The area of a square is 36 square centimeters. A rectangle has the same perimeter as the square. The length of the rectangle is
    8·1 answer
  • Who do you do the problem 7/9+1/7+3/5? please explain thoroughly.
    13·2 answers
  • Greata had a price of cloth that is 9 yards long. She cuts it into prices that are each 1/3 yard long. How many prices of cloth
    12·1 answer
  • How many solutions does 2x = 2x -9 have?
    13·1 answer
  • What does it mean in geometry when they are putting segments over each other to show proportionality? In some video about triang
    9·1 answer
  • را آزرا<br> What is the value of x in the proportion?
    13·2 answers
  • What is the area of the school crossing sign represented below?
    9·1 answer
  • Whats the answer to <br> y=3x+9
    13·1 answer
  • What is the product of (t – 4) (t? + 2t - 6)?
    13·1 answer
  • What is the converse of the statement? if p then q
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!