Mathematics, 15.08.2019 09:10 abdirahmansoloman

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

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Answer from: 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 :

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

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

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

Answer from: Quest

a. we have two

lines: y = 4-x and

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b. 4-x = 8-x^-1

x 4-x 8-x^-1

-3 7

8.33

-2 6 8.5

-1 5 9

0 4

1 3

2 2

7.5

3 1 7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:

x=-4.236

y = 4-x = 4 – (-4.236)

= 8.236

y = 8-x^-1 = .236)^-1

= 8.236

x=0.236

y = 4-x = 4 – (0.236) = 3.764

y = 8-x^-1 = 8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c. to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x and y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines. the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

Answer from: Quest

b and c

step-by-step explanation:

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