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

May 1, 2018

4

#### Explanation:

Rephrase it into math!

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

${x}^{2} + 5 x = 36$
The square is indicated with $^ 2$. If we add it to five times that number, or $5 \cdot x = 5 x$, then we get ${x}^{2} + 5 x = 36$.

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

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

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

Yay!

May 1, 2018

The number is 4.
$x = 4$

#### Explanation:

Rewrite the word problem as an equation.

${x}^{2} + 5 x = 36$

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

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:

${4}^{2} + \left(5 \cdot 4\right) - 36 = 0$
$16 + 20 - 36 = 0$
$36 - 36 = 0$

May 1, 2018

The number is $4$.

#### Explanation:

Let $x$ represent the positive number.

${x}^{2} = \text{the square of a positive number}$

$5 x = \text{five times that number}$

$= 36$ $\text{is the result}$

Put it all together and you get:

${x}^{2} + 5 x = 36$

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

${x}^{2} + 5 x - 36 = 0$

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

$\left(x - 4\right) \left(x + 9\right) = 0$

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.

${4}^{2} + 5 \cdot 4 = 36$

$16 + 20 = 36$

$36 = 36$