Question

How do you solve `x^2 - 6x = 16` by completing the square?

Answer 1

`x=-2" or "x=8`

Explanation:

`"to complete the square"`

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

`"that is add "(-6/2)^2=9" to both sides"`

`rArrx^2+2(-3)xcolor(red)(+9)=16color(red)(+9)`

`rArr(x-3)^2=25`

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

`x-3=+-5larr" note plus or minus"`

`rArrx=3+-5`

`rArrx=3-5" or "x=3+5`

`rArrx=-2" or "x=8`