please give me a solution?

Question

x²+5√5x+30

x²+5√5x+30
factorize

i really don't want the answer.....i know it
it's (x+3√5)(x+2√5)
just give me the whole solution

Answer 1

No one can

It isnt set equal to anything. All I can do is algebraically manipulate and rearrange the expression

Answer 2

If trying to find the value of x, should be in the form of an equation as follows:-
x² + 5.√5.x + 30 = 0
x = [- 5.√5 ± √(125 - 120)] / 2
x = [- 5.√5 ± √5] / 2
x = [√5.(- 5 + 1)] / 2, x = [√5.(- 5 - 1] / 2
x = - 2.√5 , x = - 3.√5
May be written as:-
(x + 2.√5).(x + 3.√5) = 0
if desired.

Answer 3

x²+5√5x+30
=x²+5√5x+(5√5/2)^2 + 30 -125 /4
=(x +(5√5/2)) ^ 2 -5/4
=(x + 5√5/2 - √5/2) (x + 5√5/2 + √5/2)
=(x + 4√5/2 ) (x + 6√5/2 )

=(x + 2√5 ) (x + 3√5 )

Answer 4

To factorize x^2 + (5 root 5)x + 30, let's look at two different methods.

Firstly, let's write this quadratic as ax^2 + bx + c.


Method One - THE QUADRATIC FORMULA

x = - b plus/minus root(b^2 - 4ac) OVER 2a

So for this quadratic a = 1; b = 5 (root 5) c = 30

put into the quadratic formula

x = -5 (root 5) plus/minus root (125 - 120) OVER 2
so x_1 = -5 (root 5) plus (root 5) ALL OVER 2
and x_2 = -5 (root 5) minus (root 5) ALL OVER 2

so x = -4 (root 5) over 2 = -2 (root 5)
and
x = -6 (root 5) over 2 = -3 (root 5).

To factorize, just write (x minus x_1)(x minus x_2)
so we get (x + 2 root5)(x + 3 root5).

Expand and we see its correct!




Method Two - completing the square. This is when you write
(x + b/2)^2 [remember in this case b = (5 root 5). Expnad the square and compare this to the quadratic you have. There will be some difference.

You'll get ==>
original quadratic = (x + b/2)^2 - some difference.
For this example we'd have
(x + (5 root 5)/2)^2 +30 - 125/4
(x + (5 root 5)/2)^2 - 5/4

The next step in this method is to use the 'difference of squares technique" to factorize this.
[difference of squares is (p^2 - q^2)=(p-q)(p+q)].
In this case
(x + (5 root 5)/2 - (root 5)/2)(x + (5 root 5)/2 + (root 5)/2)
= (x + (4 root 5)/2)(x + (6 root 5)/2 )
=(x + 2 root 5)(x + 3 root 5)

{expand to check}

This method is a little tricky!

Answer 5

The answer is 2

Answer 6

the answer is 2

Answer 7

Don't write 'factorize' on your homework or you'll likely lose points for creating a word.

just 'factor'