Mathematics, 15.08.2019 09:10, abdirahmansoloman

7k^2-16k+100=0 using completing the square ?

Answers: 1

Show answers

Answers

answered: eskarletche8

7k^2-16k+100=0

7k^2-16k=-100

Add a squared constant to both sides:

7k^2-16k+c^2=c^2-100

On the left, we wish to condense the quadratic into a squared binomial,

$(\sqrt7\,k-c)^2$

Expanding this gives

$7k^2-2c\sqrt7\,k+c^2$

which tells us

$-2c\sqrt7=-16\implies c=\dfrac8{\sqrt7}$

Then $c^2=\dfrac{64}7$ , and

$\left(\sqrt7\,k-\dfrac8{\sqrt7}\right)^2=\dfrac{64}7-100$

$\left(\sqrt7\,k-\dfrac8{\sqrt7}\right)^2=-\dfrac{636}7$

If you're looking for real-valued solutions, there are none, since the square root of a negative number doesn't exist... but if you're allowing complex-valued solutions, we can take the square root of both sides to get

$\sqrt7\,k-\dfrac8{\sqrt7}=\pm 2i\sqrt{\dfrac{259}7}$

Multiply both sides by $\sqrt 7$ to eliminate denominators, then solve for :

$7k-8=\pm 2i\sqrt{259}$

$7k=8\pm 2i\sqrt{259}$

$\boxed{k=\dfrac{8\pm2i\sqrt{259}}7}$

answered: Guest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

answered: Guest

1.0

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:50, yessijessiHaley

Name the most appropriate metric unit for each measurement

Answers: 3

continue

Mathematics, 21.06.2019 22:00, goodperson21

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.

Answers: 2

continue

Mathematics, 22.06.2019 00:50, LordBooming

Answer asap. you begin with 1/2 scoop of ice cream. since you're hungry, you ask the vendor for 2/7 more scoops of ice cream. then, you eat 5/8 scoops. how many scoops of ice cream are left on your cone? i will mark brainliest for first correct answer.

Answers: 2

continue

Mathematics, 22.06.2019 03:20, DarkKings799

What is the volume of a cardboard box that measures 1 inch by 5 inches by 7 inches? the volume of the cardboard is cubic inches. enter your answer as the number that correctly fills in the blank in the previous sentence. if necessary, round your answer to the nearest tenth, like this: 42.5