equation x- 2sqrtx = 0, solve for all values of x that satisfies the equation"?

Question

please help, stumped with this one!!!

Answer 1

x^2 = 4 x

solution 1, x = 0
then x = 4, so we have


solution 2, x = 4.

Answer 2

x= 0 ,4

Answer 3

x - 2sqrt(x) = 0
Add 2 sqrt(x) to both sides
x = 2 sqrt(x)
Squaring both sides
x*2 = 4x
Subtracting 4x from both sides and factorizing
x . (x - 4) = 0
Hence, x = 0 and (x - 4) = 0
x = 0 and x = 4

Note: please check by plugging if the values of x are valid. When you square both sides, there is a possibility that an extraneous value may come out which will not satisfy the equation. Here both values are valid.

Answer 4

The answer is 0, 4.

Now, how did they do that?

x - 2x^(1/2) = 0, multiply both sides of the equation by (x + 2x^(1/2))

(x-2x^(1/2)) (x+2x^(1/2)) = 0 (x-2x^(1/2))

x^2 - 4x = 0, now factor out the x

x(x-4) = 0

x = 0, x = 4

Check the work by plugging the answers back in...hope this helps

Answer 5

you can write x=2sqrt x (Consider xmust be >=0) Squaring both sides x^2=4x ==> x(x-4)=0 so x=0 ,x=4

Answer 6

Factor in terms of sqrtx:
sqrtx(sqrtx-2) = 0
→ sqrtx = 0 or sqrtx = 2
→ x=0 or x=4.

Answer 7

x - 2 sqrt(x) = 0

x = 2 sqrt(x)

x/2 = sqrt(x) ... Now sqaure both sides:

(x/2) * (x/2) = x

(1/4) x² = x ... Now rearrange terms

(1/4) x² - x = 0 ... Solve this quadratic.
... First kill the Fraction (mult. by 4)

x² - 4x = 0 ... Complete the Square

Answer 8

you write x-2sqrt x =0

x=2sqrt x

square this

x^2 = 4x ---> x(x-4) =0

roots x=0 x=4

It works !

Answer 9

put the entire equation to the second power, then you have:
x-squared - 4x = 0, which should be easier to solve.