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

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step-by-step explanation: