Question

solve (3x+7)^1/2=x-1

Answer 1

6

Answer 2

(3x+7)^1/2 = x-1 Square both sides since (3x+7)^1/2 is a square root
3x+7 = (x-1)^2
3x+7 = x^2-2x+1
0 = x^2-5x-6 I will rewrite this equation to get:
x^2-5x-6 = 0
(x-6)(x+1) = 0
x-6 = 0
x = 6

x+1 = 0
x = -1

The two possible solutions are x=6 and x=-1
Now you need to substitute these values to see what the solution really is

[(3)(6)+7]^1/2 = 6-1
(18+7)^1/2 = 6-1
(25)^1/2 = 6-1
5 = 5 which is a true statement and, therefore, x=6 is true (valid)

[(3)(-1)+7]^1/2 = -1-1
(-3+7)^1/2 = -1-1
(4)^1/2 = -1-1
2 is not equal to -2 and, therefore, x=-1 is not true (not valid)

Therefore, the answer is x=6