Question

**60 POINTS** How to solve step-by-step...:

#1) sqrt(3x+7) +1=x

#2) 4 3^sqrt(3x-3)^2 +2=38

Answer 1

The answer is x = 6 and I did the math in my head so fast

Answer 2

sqrt(3x+7)=x-1 One solution was found : x = 6
Radical Equation entered : √3x+7 = x-1

Step by step solution :Step 1 :Isolate the square root on the left hand side : Radical already isolated
√3x+7 = x-1

Step 2 :Eliminate the radical on the left hand side : Raise both sides to the second power
(√3x+7)2 = (x-1)2

After squaring
3x+7 = x2-2x+1

Step 3 :Solve the quadratic equation : Rearranged equation
x2 - 5x -6 = 0

This equation has two rational roots:
{x1, x2}={6, -1}
Step 4 :Check that the first solution is correct : Original equation
√3x+7 = x-1

Plug in 6 for x
√3•(6)+7 = (6)-1

Simplify
√25 = 5
Solution checks !!
Solution is:
x = 6
Step 5 :Check that the second solution is correct : Original equation
√3x+7 = x-1

Plug in -1 for x
√3•(-1)+7 = (-1)-1

Simplify
√4 = -2
Solution does not check
2 ≠ -2
One solution was found : x = 6