Solve for x pls

Question

√x-1 + 3 = x

x-1 is all under the root

 

√7-6x  + 3x = 2

7-6x is all under the root

Answer 1

1.

 

Isolate the radical term to one side.

 

√(x - 1) + 3 = x

√(x - 1) = x - 3

 

Square both sides.

 

√(x - 1) = x - 3

x - 1 = (x - 3)²

x - 1 = x² - 6x + 9

 

Combine like terms on one side.

 

x - 1 = x² - 6x + 9

0 = x² - 7x + 10

 

Factor.

 

0 = (x - 5)(x - 2)

 

Set each factor to zero and solve.

 

x - 5 = 0

x = 5

 

x - 2 = 0

x = 2

 

2. 

 

Isolate the radical term to one side.

 

√(7 - 6x) + 3x = 2

√(7 - 6x) = 2 - 3x

 

Square both sides.

 

√(7 - 6x) = 2 - 3x

7 - 6x = (2 - 3x)²

7 - 6x = 4 - 12x + 9x²

 

Combine like terms on one side.

 

7 - 6x = 4 - 12x + 9x²

0 = 9x² - 6x - 3

 

Factor.

 

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

 

Set each factor to zero and solve.

 

3x + 1 = 0

3x = -1

x = -1/ 3

 

3x - 3 = 0

3x = 3

x = 1