How do i find the solution of this equation?

Question

x + √ (2x + 1) = 2x -1?? 

Answer 1

The radical equation x + √(2x + 1) = 2x - 1

Isolate the square root on one side of the equation.

√(2x + 1) = 2x - 1 - x

√(2x + 1) = x - 1

Square both sides of the equation.

2x + 1 = (x - 1)²

2x + 1 = x² + 1 - 2x

2x + 1 - x²  -  1 + 2x =  0

- x² + 4x = 0

x² - 4x = 0

x(x - 4) = 0

Apply zero product property.

x = 0 and x - 4 = 0

x = 0 and x = 4

Check the above solutions:

For x = 0

0 + √(2(0) + 1) = 2(0) - 1

√1 ≠ - 1

For x = 4

4 + √(2(4) + 1) = 2(4) - 1

4 + √9 = 8 - 1

4 + 3 = 7

7 = 7

Solution of radical equation x = 4.