How to complete the square to find the value of x?

To complete the square you compare your equation in the form x² + bx + c = 0 to a similar equation of (x + b/2)² + c = 0. From expanding out the second equation we have x² + bx + (b/2)² + c = 0 we can see this differs from the first equation by the term (b/2)² so if we subtract (b/2)² we are back to the original equation. So the equation x² + bx + c = 0 is equal to (x + b/2)² - (b/2)² + c = 0. So to solve this we can move the terms around to get (x + b/2)² = (b/2)² - c which can then be solved by taking the square root of both sides.