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

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

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Answer 1 · 2018-05-01T02:00:21

4

Explanation:

Rephrase it into math!

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

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

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

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

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

Yay!

Answer 2 · 2018-05-01T02:02:46

The number is 4.
$x = 4$ $x = 4$

Explanation:

Rewrite the word problem as an equation.

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

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

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:

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

Answer 3 · 2018-05-01T02:05:18

The number is $4$ $4$ .

Explanation:

Let $x$ $x$ represent the positive number.

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

$5 x = five times that number$ $5x="five times that number"$

$= 36$ $=36$ $is the result$ $"is the result"$

Put it all together and you get:

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

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

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

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

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

Solve each binomial.

$x - 4 = 0$ $x-4=0$

$x = 4$ $x=4$

$x + 9 = 0$ $x+9=0$

$x = - 9$ $x=-9$

$x = - 9, 4$ $x=-9,4$

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

Check.

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

$16 + 20 = 36$ $16+20=36$

$36 = 36$ $36=36$

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

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