Answer:
Camila's favorite number is 4
Step-by-step 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
[tex]x^{2} +2x=24[/tex]
Step 2
[tex]x^{2} +2x-24=0[/tex]
solve for x
using the quadratic equation
[tex]x=-\frac{-b +-\sqrt{b^{2}-4ac } }{2a}[/tex]
a=1
b=2
c=-24
put the values into the equation
[tex]x=\frac{-2 +-\sqrt{2^{2}-4(1)(-24)} }{2(1)}\\x=\frac{-2 +-\sqrt{4+96} }{2}\\\\x=\frac{-2 +-\sqrt{100} }{2}\\\\x=\frac{-2+10}{2} \\x=\frac{8}{2} \\x=4\\[/tex]
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.
