Radical equations!?

Question

How would you solve x= rad.2x+3
*the 2x+3 is all under the radical sign
Please show work....thanx for helping me out

Answer 1

x= sqrt(2x+3)

square both sides. Memorize this rule:
sqr(a) x sqrt(a) = a

x^2 = 2x + 3

subtract 2x and 3 for bth sides to set the equation equal to 0.

x^2 - 2x + 3

now factor. Looke for two numbers that multiply to 3 and add to -2

the two numbers are -3 and 1

(x-3) (x + 1) = 0
x = 3 or -1

when you have a radical function, you have to check your answers. -1 is obviously not the answer, because when you take a square root, the answer is a positive number.

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

only 3 is the solution.

Answer 2

x= sqrt of 2x+3
square both sides of the problem

x^2=2x+3
have it in the quadratic formula for trinomials
x^2-2x-3=0

Factor if you can
(x-3)(x+1)=0

x =3 or -1
the only answer that fits the equation is x=3