If the square of a positive number is added to five times that number, the result is 36. Find the number?

Rephrase it into math!

If we let `x` equal the number, then,

`x^2+5x=36`
The square is indicated with `^2`. If we add it to five times that number, or `5*x=5x`, then we get `x^2+5x=36`.

This is a quadratic! We subtract 36 from both sides to get `x^2+5x-36=0`.

Solving it, we get `(x-4)(x+9)`.
Remember, though! The number must be positive. `x>0`.

Therefore the only possible answer is `x=4`.

Yay!

Rewrite the word problem as an equation.

`x^2 + 5x = 36`

This problem is a quadratic, stated as `x^2 + 5x - 36 = 0`

A simple solution is to find two numbers; numbers which when multiplied = -36, and when added = 5.

Our numbers are 9 and -4. So x + 9 and x - 4 are our roots, leaving x as either -9 or 4. Since our question requires a positive answer, the answer must be 4.

Check:

`4^2 + (5 * 4) - 36 = 0`
`16 + 20 - 36 = 0`
`36 - 36 = 0`

Let `x` represent the positive number.

`x^2="the square of a positive number"`

`5x="five times that number"`

`=36` `"is the result"`

Put it all together and you get:

`x^2+5x=36`

This is a quadratic equation which can be solved for `x` by setting it equal to zero.

`x^2+5x-36=0`

We can factor `x^2+5x-36` by finding two numbers that when added equal `5` and when multiplied equal `-36`. The numbers `-4` and `9` meet the criteria.

`(x-4)(x+9)=0`

Solve each binomial.

`x-4=0`

`x=4`

`x+9=0`

`x=-9`

`x=-9,4`

We need the positive value of `x`, so `x=4`

Check.

`4^2+5*4=36`

`16+20=36`

`36=36`