Question

Help with quadratic related question... MEDAL!!

Answer 1

If I have the solution to a quadratic as \((v + 60)^2 = \sqrt{20}\) then can I simplify this further into \(-6 \pm 2\sqrt{5}\)

Answer 2

sorry i meant to say \((v + 6)^2 = \sqrt{20}\)

Answer 3

@Nnesha

Answer 4

is that the original question
2sqr{5} is just solution of sqrt{20}
how did you get rid of the square root from (v+6)^2

Answer 5

i thought that I could just do the inverse to solve for v. and then i put that with the plus/minus and the square root of 20

Answer 6

in order to cancel out the square of (v+6)^2 you have to take square root both sides \[\sqrt{(v+6)^2 } = \sqrt{{2\sqrt{5}}}\]

Answer 7

how would i continue doing that?

Answer 8

hmmm is there any statement ?
all i can do is just to split it into two equation

Answer 9

so do you want the question?

Answer 10

what do you mean ? o.O
so (v+6)^2 = sqrt{20} isn't the original question ?

Answer 11

no that's like the answer to the question.. i want to know if i can further simplify this.

Answer 12

hmm okay ye i would like to see the original question

Answer 13

\(v^2 + 12v + 4 = -2\)

Answer 14

The equation

\(x^2 = k\), for non-negative \(k\) has solutions

\(x = \sqrt k\) or \(x = -\sqrt {k} \)

Answer 15

and how did you get (v+6)^2 = sqrt{20} ?????? :o

Answer 16

I think you have done something a little off while completing the square

Answer 17

i think you're working on completing the square method :o

Answer 18

ye true :P

Answer 19

oh yes sorry about that..

Answer 20

In your case, if you have

\((v + 6)^2 = \sqrt{20}\),

then the solutions are

\(v + 6 = \sqrt{\sqrt{20}}\) or \(v + 6 = -\sqrt{\sqrt{20}}\).

Answer 21

i forgot to mention that

Answer 22

and i think ur mistake was \[\rm (x+ \frac{b}{2})^2 \]
where we have to take half of the x term and then add (b/2)^2 both sides

Answer 23

@mathstudent55 Can't I put \(-6 \pm 2 \sqrt{5}\)

Answer 24

\(v^2 + 12v + 4 = -2\)

Subtract 4 from both sides:

\(v^2 + 12v = -6\)

Now you need to complete the square. Take 12, divide it by 2, and then square it. Add that to both sides.

\(v^2 + 12v + 36= -6 + 36\)

\(v^2 + 12v + 36= 30\)

\((v + 6)^2 = 30\)

\(v + 6 = \sqrt {30}\) or \(v + 6 = - \sqrt{30} \)

\(v = -6 + \sqrt {30}\) or \(v = -6 - \sqrt{30} \)

Answer 25

you do know that @Nnesha and I are saying that
\[v^2 + 12v + 4 = -2 \text{ isn't equivalent to } (v+6)^2=\sqrt{20}\]
that you have done something a just a tad bit off in the completing the square process

Answer 26

\(v + 6 = \sqrt{\sqrt{20}}\) or \(v + 6 = -\sqrt{\sqrt{20}}\)
this is same as \[\sqrt{(v+6)^2} =\sqrt{2\sqrt{5}}\]
but whatever this isn't correct
there is a mistake
(v+6)^2 =sqrt{20} <--- wrong

Answer 27

okay i will correct that but I just need to know how i can simplify it...

Answer 28

I should have this when you complete the square.

\((v + 6)^2 = 30\)

Answer 29

Look above at how to get to the correct complete the square form.
Then look below that to see how to simplify it and solve the equation.