help with math?

Question

Parentheses () = square root symbol

x = 3 + 2 (x)

Answer 1

just type it like this:
x = 3 + 2sqrt(x)

x - 3 = 2sqrt(x)

square both sides
x^2 - 6x + 9 = 4x

x^2 - 10x + 9

factor
(x-1)(x-9)

x = 1 or 9

check:
1 = 3 + 2 sqrt(1)
1 = 3 + 2(1)
1 = 5
1 is not equal to 5. so that is not the answer

9 = 3 + 2sqrt(9)
9 = 3 + 2(3)
9 = 3 + 6
9 = 9

so 9 is your answr. hope this helps

Answer 2

x = 3+2sqrt(x)
x - 3 = 2sqrt(x), square both sides

(x-3)^2 = 4x
x2 - 6x + 9 = 4x
x2 - 10x + 9 = 0
(x-9)(x-1) = 0
x = 9

as for x=1, checking in original equation, 1 is not an answer,

so the answer is x = 9

Answer 3

x = 3 + 2 (x)

step 1 set y = (x)

then you get
y*y = 3 + 2y

solve thiis for y :
y^2 -2y - 3= 0
=>
(y-3)(y+1) = 0
thus y = 3 or y = -1

back substitute the y with (x)

(x) = 3 or (x) = -1
(x)=3 is the onlly solution since sqrt of a number is never negeative
(x)=3 implies x=9

Answer 4

X=9
move the three to the opposite side. Square both sides. you get x^2-6x+9=4x.
Subtract 4x. You get x^2 -10x+9. Use the zero product property and you get the answer.

Answer 5

x = 3 + 2sqrtx
x - 2sqrtx -3 = 0
Let z = sqrtx
z^2 -2z - 3 = 0
(z-3)(z+1) = 0
z = 3, -1
x = 3^2 = 9