Question

The sum of a number and its square is 6. Find the number

Answer 1

Answer: The sum of a number and its square is 6. Find the number

Explanation:

n + n^2 = 6 n^2 + n - 6 = 0 factoring ___ (n + 3)(n - 2) = 0 n + 3 = 0 ___ n = -3 n - 2 = 0 ___ n = 2 two solutions

Answer 2

n = -3, 2

Explanation:

We're given:

• The sum of a number and its square is 6

Let the number be n.

• The sum of a number and its square is 6
• ⇒
  `n+n^2=6`

`n+n^2=6`

⇒ Move everything to one side of the equation:

`n+n^2-6=0`

⇒ Organize in
`ax^2+bx+c=0` form:

`n^2+n-6=0`

⇒ Factor:

`n^2-2n+3n-6=0\\n(n-2)+3(n-2)=0\\(n+3)(n-2)=0`

⇒ Use the zero-product property to find n:

`n+3=0\\n=-3` or
`n-2=0\\n=2`