Question

A number is four times larger then the square of half the number

Answer 1

n is 4 more than square of half of n


`n=4+ ((n)/(2))^2`

`n=4+ (n^2)/(4)`
times both sides by 4
4n=16+n²
minus 4n both sides
0=n²-4n+16
gots to use quadratic formula
for an²+bn+c=0
n=
`(-b+/- √(b^2-4ac) )/(2a)`
1n²-4n+16=0

n=
`(-(-4)+/- √((-4)^2-4(1)(16)) )/(2(1))`
n=
`(4+/- √(16-64) )/(2)`
n=
`(4+/- √(-48) )/(2)`
uh oh, we got imaginary numbers
if we simplify we get n=2+2i√3 or n=2-2i√3

that can't be right



maybe it's

`n=4+(n^2)/(2)`
times both side sby 2
2n=8+n²
minus 2n

0=n²-2n+8
factor
0=(n-4)(n+2)
st to zero

n-4=0
n=4

n+2=0
n=-2


the number is -2 or 4










if it be
`n=4+ ((n)/(2))^2` then n=2+2i√3 or 2-2i√3
if it be
`n=4+ (n^2)/(2)` then n=-2 or 4

Answer 2

I think its -2, and hope this was helpful (: