Question

Camila's favorite number is positive, and the square of her number plus twice her number

is 24. What is her favorite number?
​

Answer 1

Camila's favorite number is 4

Explanation:

Hello, I can help you with this.

you can easily solve this by constructing a equation for the situation and then to find the unknown value.

Step 1

define

Let

x= the Camila's favorite

according to the problem.

Camila's favorite number is positive,so

X≥0

and

the square of her number plus twice her number is 24

`x^(2) +2x=24`

Step 2

`x^(2) +2x-24=0`

solve for x

using the quadratic equation

`x=-\frac{-b +-\sqrt{b^(2)-4ac } }{2a}`

a=1

b=2

c=-24

put the values into the equation

`x=\frac{-2 +-\sqrt{2^(2)-4(1)(-24)} }{2(1)}\\x=(-2 +-√(4+96) )/(2)\\\\x=(-2 +-√(100) )/(2)\\\\x=(-2+10)/(2) \\x=(8)/(2) \\x=4\\`

the second x in -6, it does not work because we are looking for a positive number so the answer is

4

Have a great day.