How many, solutions does this equation have?
x² + 6x -
- 16 = 0

i don’t know

Step-by-step explanation: answer my question

Find two factors of  

16

which differ by  

6

. The pair  

8

,

2

works in that  

8

×

2

=

16

and  

8

−

2

=

6

.

Hence we find:

0

=

x

2

+

6

x

−

16

=

(

x

+

8

)

(

x

−

2

)

So  

x

=

2

or  

x

=

−

8

Alternatively, complete the square then use the difference of squares identity:

a

2

−

b

2

=

(

a

−

b

)

(

a

+

b

)

with  

a

=

(

x

+

3

)

and  

b

=

5

as follows:

0

=

x

2

+

6

x

−

16

=

(

x

+

3

)

2

−

9

−

16

=

(

x

+

3

)

2

−

25

=

(

x

+

3

)

2

−

5

2

=

(

(

x

+

3

)

−

5

)

(

(

x

+

3

)

+

5

)

=

(

x

−

2

)

(

x

+

8

)

Hence zeros  

x

=

2

and  

x

=

−

8

Plz mark me as brainlist

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}