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

##### 3 Answers

4

#### Explanation:

Rephrase it into math!

If we let

The square is indicated with

This is a quadratic! We subtract 36 from both sides to get

Solving it, we get

Remember, though! The number must be positive.

Therefore the only possible answer is

Yay!

The number is 4.

#### Explanation:

Rewrite the word problem as an equation.

This problem is a quadratic, stated as

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:

The number is

#### Explanation:

Let

Put it all together and you get:

This is a quadratic equation which can be solved for

We can factor

Solve each binomial.

We need the positive value of

Check.