Question

How do you solve using the completing the square method `x^2 – 5x + 10 = 0`?

Answer 1

`x=+-sqrt15/2 i+5/2`

Explanation:

To `color(blue)"complete the square"`

add `(1/2" coefficient of the x-term")^2" to " x^2-5x`

To retain the balance of the equation this should be added to both sides.

`rArr" add " (-5/2)^2=25/4`

`rArr(x^2-5xcolor(red)(+25/4))+10=0color(red)(+25/4)`

`rArr(x-5/2)^2=25/4-10`

`rArr(x-5/2)^2=-15/4`

Since the right side is negative, the solutions are complex.

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

`sqrt((x-5/2)^2)=+-sqrt(-15/4)`

`rArrx-5/2=+-sqrt15/2i`

`rArrx=+-sqrt15/2i+5/2`