Solve equation by completing the square

Hello from MrBillDoesMath!

x = -1 +\- sqrt(5)

Discussion:

Generally, to "complete the square",  add  (1/2) the coefficient of x, that  is (1/2)(-2) = -1, squared, to both sides of the equation:

x^2 -2x  + (-1)^2 - (-1)^2 -4  = 0       => simplify using (-1)^2 = 1

(x^2 - 2x + 1) -1 -4 = 0                      => add 5 to both sides

(x^2 - 2x + 1) = 5                               =>

(x+1)^2 = 5                                        => take square root of both sides

x+1 = +\-sqrt(5)                                 => subtract 1 from both sides

x = -1 +\- sqrt(5)

Thank you,

MrB

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.