Question

when the square of a number is added to the number trebled, the result is 108. what is the number? (solve it in quadratic context, plsss, finding it really difficult)

Answer 1

number is 'n'

square of a number means n^2
added to means plus or +
number trippled is 3n
result means equals or =
108 is 108


n^2+3n=108
minus 108 from both sides
n^2+3n-108=0
if want quadratic formula
in form
ax^2+bx+c=0
x=
`(-b+/- √(b^2-4ac) )/(2a)`
a=1
b=3
c=-108


x=
`(-3+/- √(3^2-4(1)(-108)) )/(2(1))`
x=
`(-3+/- √(9+432) )/(2)`
x=
`(-3+/- √(441) )/(2)`
x=
`(-3+/- 21 )/(2)`
x=
`(-3+21 )/(2)` or x=
`(-3- 21)/(2)`
x=
`(18 )/(2)` or x=
`(-24)/(2)`
x=9 or -12

the number is either 9 or -12

Answer 2

Hello,

Let's assume x the number

x^2+3x=108
==>x^2+3x-108=0
Δ=3²+4*108=441=21²

x= (-3+21)/2 or x=(-3-21)/2
==>x=9 or x=-12