Question

How do you solve `5x^2-10x=23` by completing the square?

Answer 1

`x=1+-sqrt(28/5)`

Explanation:

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

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

`"factor out 5"`

`5(x^2-2x)=23`

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

`5(x^2+(-1)xcolor(red)(+1))=23color(red)(+5)larr"note"`

`rArr5(x-1)^2=28`

`rArr(x-1)^2=28/5`

`color(blue)"take the square root of both sides"`

`sqrt((x-1)^2)=+-sqrt(28/5)larrcolor(blue)"note plus or minus"`

`rArrx-1=+-sqrt(28/5)`

`"add 1 to both sides"`

`rArrx=1+-sqrt(28/5)larrcolor(red)"exact solutions"`