Question

Translate to a quadratic equation, then solve using the quadratic formula.

A positive integer squared plus 5 times its consecutive integer is equal to 11. Find the integers.

Answer 1

The integer is 1

Explanation:

Required

Translate and solve

Let the positive integer be x.

So, we have;

The square of the integer is: x^2

Plus 5 times its consecutive integer is: x^2 + 5(x + 1)

Equals 11 is: x^2 + 5(x + 1) = 11

So, we have:

`x^2 + 5(x + 1) = 11`

Open bracket

`x^2 + 5x + 5= 11`

Subtract 11 from both sides

`x^2 + 5x -6= 0`

Expand

`x^2 + 6x - x-6= 0`

Factorize:

`x(x + 6) - 1(x+6)= 0`

Factor out x + 6

`(x - 1) (x+6)= 0`

Split

`x - 1 = 0\ or\ x + 6 = 0`

Solve for x in both cases

`x = 1\ or\ x = -6`

Since the number is positive, then
`x = 1`