Question

simplify the equation express the solution as a radical in the simplest form 4 sqrt x+3=x

Answer 1

is 3 in the square root as well?

Answer 2

yes it is
\[4\sqrt{x+3}=x\]

Answer 3

ok what is the /4 next to the problem for?

Answer 4

Eh..

Answer 5

You forgot to square the x.

Answer 6

@angela wait---isnt it supposed to be x^2/16 since u square both sides

Answer 7

:(:(

Answer 8

\[\sqrt{x+3} = \frac{x}{4}\]\[\implies x+3 = \frac{x^2}{16}\qquad;\; x > -3\]

Answer 9

me=??????????????? what

Answer 10

\[\implies -x^2 + 16x + 48 = 0\qquad;\; x > -3\]

Answer 11

can someone show me for the beginning please

Answer 12

Is the problem this? \[4\sqrt{x} + 3 = x\] or this \[4\sqrt{x+3} = x\]

Answer 13

You can write that as \[\sqrt{x+3}= x \div4\] . Then if you square both sides you get x+3 = x^2/16 . Do you know how to do the rest?

Answer 14

@polpak yes 2nd one

Answer 15

ok i got to \[x+3=x^2/16 \] now what

Answer 16

multiply both sides by 16

Answer 17

ok i have 16x+48=x^2

Answer 18

subtract x^2 from both sides

Answer 19

ok now i have -x^2+16x+48=0

Answer 20

use quadratic formula.

Answer 21

how do i do that

Answer 22

Are you familiar with this ?

For
\[ax^2+bx+c=0\]

\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Answer 23

oh that ok let me try to do that

Answer 24

ok yea i need help

Answer 25

what is the triangle for

Answer 26

in our case, what are :
a=?
b=?
c=?

Answer 27

a=x^2
b=16x
c=48

Answer 28

a=-x^2

Answer 29

The triangle is just a symbol for the discriminant (that radical)

Answer 30

oh okay

Answer 31

a is the coefficient of x^2. in our case a=-1

Answer 32

oh okay

Answer 33

so what are:
b=?
c=?

Answer 34

b=16x
c=48

Answer 35

\[x=-16x \pm \sqrt{16^2(-1)(48)}/2(-1)\]

Answer 36

Note that below :

a*x^2 + b*x + c = 0

a is the number in front of x^2
b is the number in front of x
and c is just a number

so:
a=-1
b=16
c=48

Answer 37

is that kinda what it is supposed to look like

Answer 38

there is no "x" . a b and c are just numbers - see their values I posted above.

Answer 39

oh okay i forgot to take that out but other than that was it okaay

Answer 40

but let's start with the discriminant first.

What is:
\[\sqrt{b^2-4ac}\]

Answer 41

\[\sqrt{16^2(-1)(48)}\]

Answer 42

crap
\[\sqrt{16^2-4(-1)(48)}\] there

Answer 43

was that right?

Answer 44

The discriminant is actually the value INSIDE the radical.

b^2-4ac


So you got
b^2-4ac=16^2+4*48=448

Answer 45

now what can you do with

\[\sqrt{448}\]

Can you take anything out of the radical ?

Answer 46

im not sure what you mean

Answer 47

\[\sqrt{448}=\sqrt{8^2*7}\]

Answer 48

oh okay now i have done that

Answer 49

so what can we take out of the radical ?

Answer 50

4

Answer 51

we have 8^2 inside the radical, so we can take 8 out of the radical

Answer 52

ok and how

Answer 53

so its 8 sqrt7 ?

Answer 54

so we will end up with this:
\[8\sqrt{7}\]

Answer 55

ok now what

Answer 56

ok so now look at the whole formula again and plug in the rest of the stuff
\[x=\frac{-b \pm 8\sqrt{7}}{2a}\]

Answer 57

okay
\[x=-16\pm8\sqrt{7}/2(-1)\]
like that

Answer 58

notice that the (-b) is supposed to be divided by (2a) as well

Answer 59

use the draw tool :)