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
Nataly_w [17]
3 years ago
7

−2x=x2−6 Rewrite the equation by completing the square.

Mathematics
1 answer:
V125BC [204]3 years ago
6 0

Answer:

(x + 1)² = 7

Step-by-step explanation:

Given:

-2x = x² - 6

We'll start by rearranging it to solve for zero:

x² + 2x - 6 = 0

The first term is already a perfect square so that's fine.  Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.

Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term.  That value will of course be 1, giving us:

x² + 2x + 1 - 1 - 6 = 0

Now can group our perfect square on the left and our constants on the right:

x² + 2x + 1 - 7= 0

x² + 2x + 1 = 7

(x + 1)² = 7

To check our answer, we can solve for x:

x + 1 = ± √7

x = -1 ± √7

x ≈ 1.65, -3.65

Let's try one of those in the original equation:

-2x = x² - 6

-2(1.65) = 1.65² - 6

- 3.3 = 2.72 - 6

-3.3 = -3.28

Good.  Given our rounding that difference of 2/100 is acceptable, so the answer is correct.

You might be interested in
Something divided by something equals 132
natta225 [31]
11 x 12 =132
i think this is the right answer
8 0
3 years ago
Maria has baked a cake for Cathy's birthday. The dimensions of the cake are 13 1/2 inches by 6 3/4 inches. The cake is going to
ycow [4]

Answer:

Step-by-step explanation:

Given:

Length = 27/4 in

Width = 27/2 in

5.55% of the cake = 5.55/100

= 1/18 

Therefore, 18 equal squares of cake where 1 piece is 5.55 % of the cake

Since, the cake is twice as long as it is wide, so that means cut half the cake (27/4 × 27/4) into 9 pieces.

Therefore, each has a side of 1/3 * 27/4

= 9/4 inches.

8 0
3 years ago
Please help its pretty easy
aleksandrvk [35]

Answer:

26/36 numbers are greater than 10

Simplify

13/18

Multiply by the chance of getting tails

13/18 x 1/2 = 13/36

13/36 your answer

26 wanted numbers / 36 amount of numbers

1 tails / 2 sides

Step-by-step explanation:

5 0
2 years ago
Use the table below to complete exercise 7
12345 [234]
C is the answer I believe
3 0
2 years ago
Kim purchased 6 small containers of potato salad and Seth purchased 2 extra large containers of potato salad. What is the differ
icang [17]

I am assuming that the attached is the complete question and we need to get the information from the table.

From the table we know the below fact:

1 \; small \; container \; of \; potato \; salad \; Weighs \; \frac{2}{8} \; pounds\\\\1 \; extra \; large \; container \; of \; potato \; salad \; Weighs \; \frac{9}{8}  \; pounds

Weight \; of \; 6 \; small \; container = 6 \times \frac{2}{8}  = \frac{12}{8}  \; pounds\\\\Weight \; of \; 2 \; Extra \; large \; container = 2 \times \frac{9}{8} \; = \; \frac{18}{8}  \; pounds

Conclusion:

The difference in weights, in pounds of Kim’s and Seth’s purchases is given below:

\frac{18}{8} - \frac{12}{8} =  \frac{18-12}{8}   = \frac{6}{8}  \\\\Simplifying \; the \; fraction \; dividing \; by \; 2 \; on \; both \; numerator \; and \; denominator\\\\ \frac{6 \div 2}{8 \div 2}  = \frac{3}{4}

Final answer : <em><u>0.75 pounds</u></em>

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the distance between (-4,-3) and (-8,2)
    10·1 answer
  • 700/200 in a terminating decimal
    8·1 answer
  • Twenty-five blue and twenty-five yellow marbles are placed in a jar. Thirty-four marbles are removed from the jar and put in a s
    10·1 answer
  • What is the direction of air resistance when an object is falling
    9·1 answer
  • Please help me. I don’t understand
    9·2 answers
  • A heated piece of metal cools according to the function c(x) = (.5)x − 11, where x is measured in hours. A device is added that
    10·1 answer
  • I need help!
    7·1 answer
  • 8 1/16-5 1/2 I need help with this.pls
    6·1 answer
  • Please fast urgent .
    9·1 answer
  • Mark moved into a new house and believes his bedroom will soon be taken over by ants. In the table shown below, Mark recorded th
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!