Question

How do you solve `x^2-2x-4=0` by completing the square?

Answer 1

`color(purple)(x = sqrt5 + 1, -sqrt5 + 1 = 3.236, -1.236`

Explanation:

`x^2 - 2x - 4 = 0`

`x^2 -2x = 4`

Add 1 to both sides,

`x^2 - 2x + 1 = 4 + 1 = 5`

`(x-1)^2 = (sqrt5)^2`

`x-1 = +- sqrt5`

`color(purple)(x = sqrt5 + 1, -sqrt5 + 1 = 3.236, -1.236`

Answer 2

`x=1+-sqrt5`

Explanation:

`"using the method of "color(blue)"completing the square"`

`• " the coefficient of the "x^2" term must be 1 which it is"`

`• " add/subtract "(1/2"coefficient of x-term")^2" to"`
`x^2-2x`

`rArrx^2+2(-1)xcolor(red)(+1)color(red)(-1)-4=0`

`rArr(x-1)^2-5=0larrcolor(blue)"add 5 to both sides"`

`rArr(x-1)^2=5`

`color(blue)"Take square root of both sides"`

`rArrx-1=+-sqrt5larrcolor(blue)"note plus or minus"`

`"add 1 to both sides"`

`rArrx=1+-sqrt5larrcolor(red)"exact solutions"`