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

4x and 6y

im not sure though

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation: