x^2+6x+9=16 solve by completing the square

Answers

Answer 1

First move the 9 to the right side by subtracting 9 from both sides.

So we have x² + 6x ___ = 7 ___.

Notice that I created a space on each side of the equation.

The space is what we need to complete the square.

The number that goes in the spaces comes from half the coefficient of the

middle term squared, which in this case is half of 6, or 3, squared, which is 9.

So we add 9 to both sides of the equation.

Once we have completed the square, out trinomial will always factor as a binomial squared, and the number that goes inside the binomial will always be half the coefficient of the middle term of the trinomial.

So we have (x + 3)² = 16.

Now square root both sides to get x + 3 = ± 4

So x + 3 = 4 or x + 3 = -4.

Solving each equation from here, we get x = 1 or x = -7.

So our solution set is {1, -7}.


Related Questions

Help&EXPLAIN

Don’t use for points or will be reported and I’ll take the points back

Answers

Answer:

x = 122

Step-by-step explanation:

An exterior angle of a triangle = sum of the other two interior angles.

x = 90 + 32

x = 122

Rafael is building a circular table with a radius of 1.75 feet. The wood costs $32.50 per square foot. How much will it cost Rafael to make the table?​

Answers

Answer:

so um your answer is in step by step

Step-by-step explanation:

I assume you just want to calculate the cost of making a circle with a diameter of 2.5 feet.

The area of a circle can be calculated using the following formula:   A = pi * r2

The radius of a circle is half of the diameter.  For this problem, the radius will be 2.5 / 2 or 1.25 feet and pi is 3.14

Then the area will be :  A= 3.14 * 1.252

A= 3.14 * 1.5625 = 4.90625 ft2

If each square foot cost $32.50, then the wood will cost $32.50 * 4.90625 = $159.45

19
Y
X
4x-3
K
>
N
W
31
Solve for x.

Answers

Answer:

3123

Step-by-step explanation:

sana makatulong ❤❤

Craig treated his sister to lunch while visiting her in Campbell. Their lunch cost $40, and the sales tax in Campbell is 5%. If Craig left a 15% tip on the $40, how much in total did he pay?
Pleasee give correct

Answers

Answer:

$48

Step-by-step explanation:

5% of 40 = 2 and 15% of 40 = 6. 6 + 2 = 8. 40 + 8 = $48.

What is the midpoint of AB?

Answers

Answer:

the answer is weenie I THINK i coudl be wrong tho

Step-by-step explanation:

:)

A square rug has an area of 121 ft?. Write the side length as a square root. Then decide if the side
length is a rational number.
HELP ASAP

Answers

Square root of 121 which is 11

What is the answer plz help

Answers

Answer:

same khan is the worst

Step-by-step explanation:

Answer:

the answer is b.) (4a + 12) + (6x + 9) = 71

What is 9/10-6/10 or can you not do it?

Answers

Answer:

3/10

Step-by-step explanation:

9-6=3

both fractions have the same denominator so they keep it

9/10 - 6/10 = 3/10

3/10 is also 0.33

(6th grade)
i would really appreciate if someone could help me, and tell me how you got the answer, along with the steps !!

Answers

the answer is to this is, 1. :)

Answer:

-4

Step-by-step explanation:

-8×-8/-8+-8

-8•(-8)/-16

-8•8/16

-8/2

-4

Lines AB and CD are parallel. If 26 measures (4x - 34), and 28 measures 106°, what is the value of x?
A. x = 17
B. x=254
C. x=27
D. x= 106

Answers

Answer:

x = 27

Step-by-step explanation:

(4x-34)+106 = 180 because they are supplementary angles

subtract 106 from each side

4x-34 = 74

add 34 to each side

4x = 108

divide both sides by 4

x = 27

Mr. Alpert’s house has 40 windows. Kids playing baseball outside the house broke 10% of the windows.

Answers

Answer:

Step-by-step explanation:

Number  of windows broken = 10% of 40

                                               [tex]= \frac{10}{100}*40\\= 4[/tex]

Answer:

4 windows are broken

Step-by-step explanation:

STAAR
2. Sharon is buying a circular rug for her living room. The diameter of the rug is 8 feet.
Which measurement is closest to the area of the rug in square feet?
A 200.96 square feet
B. 50.24 square feet
C. 25.12 square feet
D. 12.56 square feet

Answers

Answer:

B.50.24

8ft is equivalent to 64ft²

Answer:

50.24

Step-by-step explanation:

5(3x - 7 + 4y)
*
+
Your answer

Answers

Answer:

15x - 35 + 20y

Step-by-step explanation:

distribute

5 x 3x = 15x

5 x -7 = -35

5 x 4y = 20y

answer- 15x-35+20y
hope it helps;)

please help me please please

Answers

For some question u can get from photo math use that app

Find x and the indicated sides.
Find x. *
5 points
S
X -
4
14
V
* - 6
R
T
Your answer
This is a required question

Answers

Answer: Can’t solve without picture.

Step-by-step explanation:

You should add a picture or at least draw it. It can’t be solved without it because the sides need to correlate together.

what is 240 x 343 x 234 x 123 x 23 - 89

Answers

the answer is 54494687431
The answer is 54,494,687,431

Why I'm so happy today?​

Answers

it’s raining tacosssssss

Answer:

ldk and I'm jealous

Step-by-step explanation:

Thanks for the free points, and have a nice day! :)

Marie made the box plot below to display a set of data. Which set of data could the box plot
represent?

Answers

Answer:

(5, 6, 10, 12, 13, 15, 17, 25, 30, 35) would be your best answer.

Step-by-step explanation:

The graph of a linear function and an exponential function is shown below.
When x = 3, the linear function and the exponential function are equal. Which of these statements is true?
The linear function never exceeds the exponential function.
The exponential function never exceeds the linear function.
The linear function exceeds the exponential function for values of x that are greater than 3.
The exponential function exceeds the linear function for values of x that are greater than 3.

Answers

Answer:

D

Step-by-step explanation:

Lamar went to a baseball game. The game started at
11;50AM, and it was 3 hours 39minutes long. When did the game end?

Answers

3:29

11:50 + 3 hours = 2:50
2:50+ 39 mins = 3:29

Answer:

The game ends at 2:39

Step-by-step explanation:

11:50 + 3 hours (3:00) = 2:00

2:00+ 0:39 = 2:39

find c. (geometry) plz help

Answers

Answer:

14.9 cm

Step-by-step explanation:

[tex] \frac{ \sin(12) }{10} = \frac{150}{a} = \frac{ \sin(18) }{c} \\ c = \frac{10 \times \sin(18) }{ \sin(12) } = \\ c = \frac{3.09}{0.2079} = 14.86 = 14.9[/tex]

14.9 is the answer the person in the top is right

find the value of x

a. 4
b. 9
c. 18
d. 14

Answers

A. 4
The degree has to equal 180 so 180-140=40 40=(10)(4)

Answer:

4

Step-by-step explanation:

We know that this is a supplementary angle, which means the sum of two angles is 180 degrees.

The Equation would then be:

140+10x=180

All you need to do is solve for x.

140+10x=180

-140         -140 (Subtract 140 from both sides)

        10x=40   (Divide by 10)

           x=4

A building is 20 feet tall and cast a 12 foot shadow, and a person who is standing right next to the building casts a 3 foot shadow.How tall would the person be?

Answers

Answer:

5 feet tall

Step-by-step explanation:

I want to just get in with life.

Answers

Answer:

The equation would be y = -2x + 1

Step-by-step explanation:

All you have to do is put it in the form y = mx + b where m is the slope and b is the y-intercept (for example, the equation y= 2x + 1 has a slope of 2 and a y-intercept of 1.)

Since you have slope, or m, = -2 and the y-intercept, or b, = 1, the equation would be y = -2x + 1

The answer would be y=-2x + 1

(x - 1) (x – 12) = 0
What’s the value of X?

Answers

Answer:

either 1

or 12

(sorrryy if its not correct:( )

Step-by-step explanation:

Solve 7k÷3=21 Math Problem

Answers

Do you mean 7000? Or k as a variable?

Answer:

k = 9

Step-by-step explanation:

do you need an explantion?

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Answers

Answer:

I thinks .... x ... to ...........

Step-by-step explanation:

Can I get brainlest

Answer: ...

Step-by-step explanation:

Which of the following are valid names for the triangle below? Check all that
apply.

Answers

Answer:

You´re correct.

Congrats.

Thomas is making a budget for his food and meal plan for dinners during his 7-night business trip. He is reimbursed at most $200. The first night he spent $38. Write and solve and inequality to represent the amount he can spend on the
other 6 nights.​

Answers

Answer:

x≤27

Step-by-step explanation:

It would be less than and equal to. The problem would be 6x + 38 ≤ 200. Hope this helps, I'm just a lonely 7th grader, it might be wrong, but it might be right at the same time. Bye, have a great day!

Please help me. Thanks. Whoever gives me the right answer, I will mark them as the brainiest.

Answers

Answer:

None

Step-by-step explanation:

I don't see any repeating #'s on the bar graph.

There are only: 22, 4, 25, 21

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