Six times a positive number when added to the square of the number will produce 16. What is the number?

Question

How do you come to the conclusion?

Answer 1

2 -
6 X 2 = 12
+ 2 X 2 =16

Answer 2

Let x = the positive number

read it step by step
"Six times a positive number "
6*x
"when added to the square of the number "
+ x^2
" will produce 16"
= 16
"What is the number" means solve for x

6x + x^2 = 16
subtract 16 from both sides
6x + x^2 -16 = 16 - 16
6x +x^2 -16 = 0
since addition is commutative, rearrange the equation into ax^2 + bx + c = 0 form
x^2 + 6x - 16 = 0
factor - what numbers multiply to -16 and add up to 6?
8 and -2
(x+8)(x-2) = 0
x+8 = 0; x = -8 and
x-2 =0; x = 2
so x can be -8 or 2
but reread the problem - "a positive number "
so x must be positive (x>0)
so x cannot be -8
it must be 2

answer: 2

Answer 3

2

Answer 4

My answer is 2.

Let "x" be the unknown number:

16 = (6)(x) + (x)(x)
16 = (6)(2) + (2)(2)
16 = 12 + 4

Trial and error. I started thinking of a number which, when multiplied by 6 would get a product less than 16 so I could add that product to the square of that same missing number.

Answer 5

The number you require is 2.

6 x 2 = 12 + 2^2 = 16

Answer 6

First let the noumber be x,
Acoording to the question,
6x + x^2 = 16
or, x^2 + 8x -2x - 16 = 0
or, x(x + 8) -2(x + 8) =0
or, (x - 2)(x + 8) = 0
Therefore x=2 or -8.
Since the number is positive the number is 2.

Answer 7

Two (2)

6 x 2 =12
2 x 2 = 4

Answer 8

2.

Answer 9

The number is 2. Have fun with math!

Answer 10

2*6=12
add
2*2=4
ans 16